For positive integers , consider: *'If is divisible by 12, then is divisible by 6.'* Which of these is correct?
Answer and explanation
Correct answer: A. The statement is true and its converse is true
- Step 1: If then , so is even, and , so (as is prime). Being even and a multiple of makes a multiple of : the statement is true.
- Step 2: Conversely, if then , so : the converse is true as well.
Answer
The statement is true and its converse is true.
Why not the others: Neither direction has a counterexample: for , is divisible by ; for or , is or , not divisible by .
Practise more Truth of statements and their converses.
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More Truth of statements and their converses questions
- For real , consider: *'If , then .'* Which of these is correct?
- For whole numbers , consider: *'If is divisible by 4, then is even.'* Which of these is correct?
- For real numbers and , consider: *'If and are both positive, then is positive.'* Which of these is correct?
- For real , consider: *'If , then .'* Which of these is correct?
- For whole numbers , consider: *'If is odd, then is odd.'* Which of these is correct?
- For whole numbers , consider: *'If is prime, then is odd.'* Which of these is correct?