Using Logic Operators

Logic Operators

Logic operators are used to combine boolean expressions. The most common ones are listed in the table below.

Operator	Name	Description	Example
`!`	not	evaluates to `true` if the boolean expression is `false` and `false` if the boolean expression is `true`.	`!(3 > 5)` evaluates to `true` since `3 > 5` evaluates to `false`. `!(5 > 3)` evaluates to `false` since `5 > 3` evaluates to `true`.
`&&`	and	evaluates to `true` if both boolean expressions evalute to `true` and `false` if one or both boolean expressions evaluate to `false`.	`true && true` evaluates to `true`. `true && false` evaluates to `false`. `false && true` evaluates to `false`. `false && false` evaluates to `false`.
`\|\|`	or	evaluates to `true` if at least one of the boolean expressions evalute to `true` and `false` if both boolean expressions evaluate to `false`.	`true \|\| true` evaluates to `true`. `true \|\| false` evaluates to `true`. `false \|\| true` evaluates to `true`. `false && false` evaluates to `false`.

Truth Tables

Boolean expressions can be evaluated by using truth tables. A truth table lists all the possible values and the associated output.

Not (!) Operator

When evaluating !a, there are two possible combinations:

a can be true
a can be false

Truth Table for ! Expression.

And (&&) Operator

When evaluating a && b, there are four possible combinations:

a and b can both be true
a can be true and b can be false
a can be false and b can be true
a and b can both be false

Truth Table for && Expression.

Or (||) Operator

When evaluating a || b, there are four possible combinations:

a and b can both be true
a can be true and b can be false
a can be false and b can be true
a and b can both be false

Truth Table for || Expression.

Your Turn

Try these out in the Java Playground.

Make predictions for the values of value1, value2, and value5.
Run the code to check your predictions.
What do you notice about the value of value1 and value2? Why is this the case?
Add statements for:
- value1 or value2
- value3 and value4
- value3 or value4
Make predictions for the newly written statements.
Run the code to check your predictions.

!(3 < 5) is equivalent to 3 >= 5. When the not (!) operator is used on an expression with a relationship operator, the equivalent expression is uses the opposite relational operator. The opposite of less than is greater than or equal to. The opposite of greater than is less than or equal to.

DeMorgan's Law

DeMorgan's Law applies in situations when a not (!) operator is being used in combination with either the and (&&) or the or (||) operators.

Truth Table to Prove DeMorgan's Law

Rule	Description	Example
`!(value1 && value2)`	evaluates to `!value1 \|\| !value2` where `value1` and `value2` are boolean expressions.	`!((5 > 7) && (3 !=0))` is equivalent to `(5 <= 7) \|\| (3 == 0)`
`!(value1 \|\| value2)`	evaluates to `!value1 && !value2` where `value1` and `value2` are boolean expressions.	`!((val + 5 <= 0) \|\| (5 == 5))` is equivalent to `(val + 5 > 0) && (5 != 5)`

Short-Circuit Evaluation

If the value of a boolean expression that involves a logic operator can be determined based on only the first boolean expression, the second boolean expression is not evaluated.

And (&&) Operator Short-Circuit

If the first expression evaluates to false, the expression with the && operator evaluates to false.

This example is a popular use of short-circuit for &&. If the value of numGrades is 0, we would get a divide by 0 error when attempting totalGrades / numGrades. Checking that numGrades is not 0 before performing division can prevent this error. Try it out! Run the code as is, and then change the value of numGrades to 0.

Your Turn

Make predictions for the values of value1, value2, and value5.
Run the code to check your predictions.
Modify the code to compute the division and then check to see if numGrades is equal to 0.

Resources

Practice: Using Logic Operators