The contrapositive of the statement 'If a number is divisible by 9, then it is divisible by 3' is:

Solution

1. Identify the original statement as 'If $p$, then $q$', where $p$ is 'a number is divisible by 9' and $q$ is 'a number is divisible by 3'.
2. The contrapositive of 'If $p$, then $q$' is defined as 'If $\neg q$, then $\neg p$'.
3. Negate the conclusion $q$ to get 'a number is not divisible by 3' and negate the hypothesis $p$ to get 'a number is not divisible by 9'.
4. Combine these to form the statement: 'If a number is not divisible by 3, then it is not divisible by 9'.
5. Hence the answer is (C).