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HTML
475 lines
8.7 KiB
HTML
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<h1>Lecture for February 6th</h1>
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<h2>If Statements -- Cont.</h2>
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<p>Inside the parenthesis of the <code>if</code> statement must be a boolean expression. This is an expression that evaluates to either <code>true</code> or <code>false</code>. We can do more complex boolean expressions through logical operators.</p>
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<h2>Logical Operators</h2>
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<p>NOT <code>!a</code> this is true when <code>a</code> is false</p>
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<p>AND <code>a && b</code> this is true when both operands are true</p>
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<p>OR <code>a || b</code> this is true when either a is true OR b is true</p>
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<h2>Truth Tables</h2>
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<ul>
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<li>Show all possible outcomes</li>
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<li>It breaks the expression down into parts</li>
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</ul>
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<h3>Not</h3>
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<p>Let's look at the most simplest case. Not.</p>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>!a</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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</tr>
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</tbody>
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</table>
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<h3>AND</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>a && b</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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</tbody>
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</table>
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<p>Notice here that <code>a && b</code> is only true when both <code>a</code> and <code>b</code> are true.</p>
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<h3>OR</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>a \</th>
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<th>\</th>
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<th>b</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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</tbody>
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</table>
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<p>Notice here that <code>a || b</code> is only false when both <code>a</code> and <code>b</code> are false.</p>
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<h2>Precedence (Order of Operations)</h2>
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<table>
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<thead>
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<tr>
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<th></th>
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<th></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>Parenthesis</td>
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<td><code>()</code></td>
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</tr>
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<tr>
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<td>Logical Not</td>
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<td><code>!</code></td>
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</tr>
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<tr>
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<td>Arithmetic Operators</td>
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<td><code>*</code> <code>/</code> <code>%</code> <code>+</code> <code>-</code></td>
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</tr>
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<tr>
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<td>Relational Operators</td>
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<td><code><</code> <code><=</code> <code>></code> <code>>=</code></td>
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</tr>
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<tr>
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<td>Equality and Inequality operators</td>
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<td><code>==</code> <code>!=</code></td>
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</tr>
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<tr>
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<td>Logical AND</td>
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<td><code>&&</code></td>
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</tr>
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<tr>
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<td>Logical OR</td>
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<td><code>||</code></td>
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</tr>
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</tbody>
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</table>
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<h2>Playing with Truth Tables Example</h2>
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<h3>a && !b</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>!b</th>
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<th>a && !b</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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</tbody>
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</table>
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<h3>!a || b</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>!a</th>
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<th>!a \</th>
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<th>\</th>
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<th>b</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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</tr>
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</tbody>
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</table>
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<h3>!(a || b && c)</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>c</th>
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<th>b && c</th>
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<th>a \</th>
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<th>\</th>
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<th>(b && c)</th>
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<th>!(a \</th>
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<th>\</th>
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<th>b && c)</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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</tr>
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</tbody>
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</table>
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<h3>!a || b && c</h3>
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<table>
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<thead>
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<tr>
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<th>a</th>
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<th>b</th>
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<th>c</th>
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<th>!a</th>
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<th>b && c</th>
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<th>!a \</th>
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<th>\</th>
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<th>b && c</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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<td>true</td>
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</tr>
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<tr>
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<td>true</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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</tr>
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<tr>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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</tr>
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<tr>
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<td>false</td>
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<td>false</td>
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<td>false</td>
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<td>true</td>
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<td>false</td>
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<td>true</td>
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</tr>
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</tbody>
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</table>
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<h2>Distributive Property of Logical Operators</h2>
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<p>The following statements are equivalent</p>
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<p><code>!(a && b)</code> is equivalent to <code>!a || !b</code></p>
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<p>Notice how when you distribute the <code>!</code> you have to flip the operand as well. <code>&&</code> becomes <code>||</code></p>
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<p>Same is true for the following example</p>
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<p><code>!(a || b)</code> is equivalent to <code>!a && !b</code></p>
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<p><code>!(a || b && c)</code> is equivalent to <code>!a && (!b || !c)</code></p>
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<h2>Short Circuit Evaluation</h2>
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<p>In an <code>&&</code> (AND) statement, if the left side is <code>false</code>, there is no need to evaluate the right side. Since it's going to be false anyways!!</p>
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<pre><code class="language-java">false && true; // FALSE no matter what the right side is</code></pre>
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<p>In an <code>||</code> (OR) statement, if the left side is `true, there is no need to evaluate the right side. Since it's going to be true by default!!</p>
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<pre><code class="language-java">true || false; // TRUE no matter what the right side is</code></pre>
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<p>Java takes this shortcut by default for efficiency reasons</p>
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