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