The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to

  • A
    $3^2 = 10$ and $I$ do not get second prize
  • B
    $3^2 = 10$ or $I$ do not get second prize
  • C
    $3^2 \neq 10$ or $I$ get second prize
  • D
    None of these

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$p$: If $7$ is an odd number,then $7$ is divisible by $2$.
$q$: If $7$ is a prime number,then $7$ is an odd number.
If $V_1$ and $V_2$ are the respective truth values of the contrapositive of $p$ and $q$,then $(V_1, V_2) \equiv$

$\sim (p \wedge q)$ is equal to .....

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Let $p$ and $q$ stand for the statements "$2 \times 4 = 8$" and "$4$ divides $7$" respectively. Then the truth values of the following biconditional statements are:
$(i)$ $p \leftrightarrow q$
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$(iv)$ $\sim p \leftrightarrow \sim q$

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