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 \
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 \
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 \	\
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 \
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!!

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!!

true || false; // TRUE no matter what the right side is

Java takes this shortcut by default for efficiency reasons