Exams › JEE Main › Maths

Examine the statements below: p: x and y are integers, and both are odd. q: the product xy is odd. Which of the following is correct?

1. p implies q is true
2. not q implies p is true
3. Both (a) and (b)
4. Neither (a) nor (b)

Correct answer: Neither (a) nor (b)

Solution

The statement 'p implies q' is true because the product of two odd integers is always odd, making option A correct. However, 'not q implies p' is false because the product being even does not necessarily mean both integers are odd; one could be even. Therefore, both A and B cannot be true, leading to the conclusion that neither statement is correct.

Related JEE Main Maths questions

• Let $T(k)$ denote the claim that $1+3+5+\cdots+(2k-1)=k^2+10$. Which statement below is correct?
• Let $S(k)$ denote the sum $1+3+5+\cdots+(2k-1)$, and suppose it is given by $k^2+3$. Which statement below is true?
• For every natural number $n$, which of the following inequalities is true?
• Let \(p\), \(q\), and \(r\) be arbitrary logical propositions. Which of the following equivalences is correct?
• The proposition \(~(p\to q)\to[(\sim p)\lor(\sim q)]\) is best classified as
• For integers $m$ and $n$, each exceeding 1, let the statements be: $P$: $m$ is a divisor of $n$; $Q$: $m$ is a divisor of $n^2$; and $R$: $m$ is a prime number. Which of the following implications is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →