Which of the following are tautology?
A. $(p \lor r) \rightarrow p$
B. $p \rightarrow (p \land r)$
C. $\sim p \rightarrow (p \rightarrow r)$
D. $(p \land r) \rightarrow (p \rightarrow r)$
E. $\sim(p \rightarrow r) \rightarrow p$
🎥 Video solution / Text Solution of this question is given below:
A: False when $r=1, p=0$ → Not tautology
B: False when $p=1, r=0$ → Not tautology
C:
$\sim p \rightarrow (p \rightarrow r)$
Always true → Tautology
D:
$(p \land r) \rightarrow (p \rightarrow r)$
Always true → Tautology
E:
$\sim(p \rightarrow r) \rightarrow p$
Always true → Tautology
Thus tautologies:
C, D, E