The statement $( p \rightarrow( q \rightarrow p )) \rightarrow( p \rightarrow( p \vee q ))$ is
a contradiction
equivalent to $( p \wedge q ) \vee(\sim q )$
a tautology
equivalent to $( p \vee q ) \wedge(\sim p )$
Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is
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
The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to
The statement $\sim[p \vee(\sim(p \wedge q))]$ is equivalent to
The contrapositive of the statement "I go to school if it does not rain" is