Consider the statement: 'If a whole number is divisible by 6, then it is divisible by 3.' Which of the following is its contrapositive?
Answer and explanation
Correct answer: D. If a whole number is not divisible by 3, then it is not divisible by 6
- Step 1: Let be 'divisible by 6' and be 'divisible by 3'. The statement is .
- Step 2: The contrapositive of is : 'not divisible by 3' implies 'not divisible by 6'.
- Step 3: A statement and its contrapositive are logically equivalent.
Answer
If a whole number is not divisible by 3, then it is not divisible by 6.
Why not the others: 'If divisible by 3 then divisible by 6' is the converse and is false (9 is a counterexample); 'if not divisible by 6 then not divisible by 3' is the inverse and is also false (3 is a counterexample); 'divisible by 6 and not by 3' is the negation of the original; 'if divisible by 3 then not divisible by 6' is false for 6.
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