The first step of an indirect proof is to assume the opposite, or negation, of the given statement.
Example Solution: 6 is an irrational number.
Practice makes perfect
The first step of an indirect proof is to assume the opposite, or negation, of the given statement. Let's think about the given statement.
Statement
If a rational number is any number that can be expressed as ab, where a and b are integers and b ≠0, then 6 is a rational number.
The conclusion of the conditional statement is 6 is a rational number. To write a negation of the given statement, we need to consider how to say its opposite. Typically this can be done using the word not.
Negation of the Statement
6 is not a rational number.
There is often more than one possibility for a negation statement. Let's look at another example.
