Which of the following is true
$p \Rightarrow q \equiv \;\sim p \Rightarrow \;\sim q$
$\sim (p \Rightarrow \;\sim q) \equiv \;\sim p \wedge q$
$\sim (\sim p \Rightarrow \,\sim q) \equiv \sim p \wedge q$
$\sim (p \Leftrightarrow q) \equiv [\sim (p \Rightarrow q) \wedge \sim (q \Rightarrow p)]$
Which of the following Boolean expression is a tautology ?
The number of values of $r \in\{p, q, \sim p , \sim q \}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, 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
If $p, q, r$ are simple propositions with truth values $T, F, T$, then the truth value of $(\sim p \vee q)\; \wedge \sim r \Rightarrow p$ is
Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard