Consider the statement: "For an integer $n$,if $n^{3}-1$ is even,then $n$ is odd." The contrapositive statement of this statement is
- AFor an integer $n$,if $n^{3}-1$ is not even,then $n$ is not odd.
- BFor an integer $n$,if $n$ is even,then $n^{3}-1$ is odd.
- CFor an integer $n$,if $n$ is odd,then $n^{3}-1$ is even.
- DFor an integer $n$,if $n$ is even,then $n^{3}-1$ is even.
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Similar Questions
If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...
$\sim (p \vee (\sim q))$ is equal to .......
Easy
View SolutionThe number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,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.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.
The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$
DifficultMHT CET 2026
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