Question

Which of the following propositions is a tautology

• A. $(p\wedge q)\to q$
• B. $p\vee (q\to p)$
• C. $p\vee (p\to q)$
• D. Both (a) and (c)

Answer 1

The correct option is D Both (a) and (c)

$\begin{array}{cccccccc}q& p& q\to p& p\to q& p\wedge q& (p\wedge q)\to q& p\vee (q\to p)& p\vee (p\to q)\\ T& T& T& T& T& T& T& T\\ T& F& F& T& F& T& F& T\\ F& T& T& F& F& T& T& T\\ F& F& T& T& F& T& T& T\end{array}$


Clearly from the truth table, we can conclude that the truth values of $p\vee (p\to q)$ and $(p\wedge q)\to q$ are always true. Hence, they are tautology.