If $p$ and $q$ are simple propositions, then $p \Leftrightarrow \sim \,q$ is true when
$p$ is true and $q$ is true
Both $p$ and $q$ are false
$p$ is false and $q$ is true
None of these
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :
The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is
If $\mathrm{p} \rightarrow(\mathrm{p} \wedge-\mathrm{q})$ is false, then the truth values of $p$ and $q$ are respectively
Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then
Which of the following Boolean expressions is not a tautology ?