Let $S$ be a non-empty subset of $R$. Consider the statement $p : x \in S$ is a rational number such that $x > 0$. Which of the following is the negation of $p$?
- A$x \in S$ is a rational number such that $x \leq 0$.
- B$x \in S$ is not a rational number such that $x \leq 0$.
- CEvery rational number $x \in S$ satisfies $x \leq 0$.
- D$x \in S$ and $x \leq 0 \Rightarrow x$ is not a rational number.
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Similar Questions
Consider the following statements:
$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?
$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?
Which of the following is a statement?
Medium
View Solution$\sim[(p \vee \sim q) \rightarrow (p \wedge \sim q)] \equiv$
Which of the following statements is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
Which statement given below is a tautology?
DifficultJEE MAIN 2023
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