For whole numbers , consider: *'If is divisible by both 4 and 6, then is divisible by 12.'* Which of these is correct?
Answer and explanation
Correct answer: B. The statement is true and its converse is true
- Step 1: If is divisible by and then it is divisible by their lowest common multiple, : the statement is true.
- Step 2: The converse holds too: a multiple of is a multiple of both and (as ).
Answer
The statement is true and its converse is true.
Why not the others: Since , divisibility by both numbers is equivalent to divisibility by , so neither direction has a counterexample; the product is not needed.
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?