Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is
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.
Similar Questions
Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$
Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.
Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$
Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
- [JEE MAIN 2016]
For the statements $p$ and $q$, consider the following compound statements :
$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
For the statements $p$ and $q$, consider the following compound statements :
$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
- [JEE MAIN 2021]
The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to
The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to
- [JEE MAIN 2019]
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
- [JEE MAIN 2021]