The 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
$1$
$2$
$3$
$4$
The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to
If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively
Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is
Negation of $p \wedge (\sim q \vee \sim r)$ is -
Consider the following two statements :
$P :$ lf $7$ is an odd number, then $7$ is divisible by $2.$
$Q :$ If $7$ is a prime number, then $7$ is an odd number.
lf $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of $Q,$ then the ordered pair $(V_1, V_2)$ equals