The contrapositive of $(p \vee q) \Rightarrow r$ is

  • A
    $r \Rightarrow (p \vee q)$
  • B
    $\sim r \Rightarrow (p \vee q)$
  • C
    $\sim r \Rightarrow (\sim p \wedge \sim q)$
  • D
    $p \Rightarrow (q \vee r)$

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Write the converse of the following statement:
If a number $n$ is even,then $n^{2}$ is even.

The statement $A$ $\rightarrow (B$ $\rightarrow A)$ is equivalent to

The statement pattern $[(p \vee q) \wedge \sim p] \wedge (\sim q)$ is

Statement-$I$: $\sim (p \leftrightarrow q)$ is equivalent to $(p \wedge \sim q) \vee (q \wedge \sim p)$.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \geq 1$.

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