For real numbers and , consider: *'If and are both positive, then is positive.'* Which of these is correct?
Answer and explanation
Correct answer: D. The statement is true and its converse is false
- Step 1: The statement is true: the product of two positive numbers is positive.
- Step 2: The converse, 'if then and are both positive', is false: gives .
Answer
The statement is true and its converse is false.
Why not the others: The converse fails for two negative numbers; the options calling the statement false are wrong since positive times positive is positive.
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 , 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?
- For real , consider: *'If , then .'* Which of these is correct?