Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
$\sim(\mathrm{q} \rightarrow \mathrm{p})$
$\sim \mathrm{p} \rightarrow \sim \mathrm{q}$
$\sim(\mathrm{p} \rightarrow \sim \mathrm{q})$
$\sim(p \rightarrow q)$
Which of the following Boolean expressions is not a tautology ?
The negation of the statement
''If I become a teacher, then I will open a school'', is
For integers $m$ and $n$, both greater than $1$ , consider the following three statements
$P$ : $m$ divides $n$
$Q$ : $m$ divides $n^2$
$R$ : $m$ is prime,
then true statement is
The negation of $(p \wedge(\sim q)) \vee(\sim p)$ is equivalent to
Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively