For whole numbers , consider: *'If is odd, then is odd.'* Which of these is correct?
Answer and explanation
Correct answer: A. The statement is true and its converse is true
- Step 1: The statement is true: if were even, would be even, so odd forces odd .
- Step 2: The converse, 'if is odd then is odd', is also true: is odd.
Answer
The statement is true and its converse is true.
Why not the others: Neither direction has a counterexample: the product of two odd numbers is always odd, and the square of an even number is always even.
Practise more Truth of statements and their converses.
Free questions with an explanation for every one, and full timed TMUA mock tests.
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 prime, then is odd.'* Which of these is correct?
- For real , consider: *'If , then .'* Which of these is correct?