Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is
For an integer $n ,$ if $n ^{3}-1$ is not even, then $n$ is not odd
For an integer $n,$ if $n$ is even, then $n^{3}-1$ is odd.
For an integer $n ,$ if $n$ is odd, then $n ^{3}-1$ is even.
For an integer $n ,$ if $n$ is even, then $n ^{3}-1$ is even.
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :
Dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is
The contrapositive of the statement "If you will work, you will earn money" is ..... .
Which of the following Boolean expressions is not a tautology ?
The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge \sim q} \right)$