Which of the following Boolean expression is a tautology ?
$(p \wedge q) \vee(p \vee q)$
$(p \wedge q) \vee(p \rightarrow q)$
$(p \wedge q) \wedge(p \rightarrow q)$
$( p \wedge q ) \rightarrow( p \rightarrow q )$
Which of the following Venn diagram corresponds to the statement “All mothers are women” ($M$ is the set of all mothers, $W$ is the set of all women)
Statement $-1$ : The statement $A \to (B \to A)$ is equivalent to $A \to \left( {A \vee B} \right)$.
Statement $-2$ : The statement $ \sim \left[ {\left( {A \wedge B} \right) \to \left( { \sim A \vee B} \right)} \right]$ is a Tautology
Which of the following statements is a tautology?
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 $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is