Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is

  • [JEE MAIN 2020]
  • A

    For an integer $n ,$ if $n ^{3}-1$ is not even, then $n$ is not odd

  • B

    For an integer $n,$ if $n$ is even, then $n^{3}-1$ is odd.

  • C

    For an integer $n ,$ if $n$ is odd, then $n ^{3}-1$ is even.

  • D

    For an integer $n ,$ if $n$ is even, then $n ^{3}-1$ is even.

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'If a function $f$ is differentiable at $a$, then it is also continuous at $a$', is

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The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :

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If the truth value of the statement $p \to \left( { \sim q \vee r} \right)$ is false $(F)$, then the truth values of the statement $p, q, r$ are respectively

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Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

  • [AIEEE 2009]