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

  1. 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.
  2. 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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