Negations of Boolean Assertions

A Boolean assertion is simply an expression that results in a true or false answer. For example,

• a > 5

• 0 == b

• a <= b

are all statements that will result in a true or false answer.

To negate a Boolean assertion means to write the opposite of a given Boolean assertion. For example, given the following Boolean assertions noted as A, the corresponding negated statements are the result of applying the ! operator to A.

Notice that negations of Boolean assertions can be used to re-write code. For example:

if  (!(x < 5))  
    // do something...

can be rewritten as

if  (x >= 5)  
    // do something ...

This is important because we understand positive statements much more easily than statements that contain one or more !s.