@Pragy Agarwal Thank you for correcting me. I understood the mistake I made.

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59 votes

Best answer

**Cannot be determined.**

From the axiom $\lnot p \to q$, we can conclude that $p \vee q$.

So, either $p$ or $q$ must be TRUE.

$$\begin{align}

&\lnot p \lor (p \to q)\\[1em]

\equiv& \lnot p \lor ( \lnot p \lor q)\\[1em]

\equiv&\lnot p \lor q

\end{align}$$

Since nothing can be said about the Truth value of $p$, it implies that $\lnot p \lor q$ can also be True or False.

Hence, the value cannot be determined.

1

5 votes

given that $ \lnot p \to q$ is true

A proposition can have only 2 possible values namely true or false. Here I feel “cannot be determined”(option D) is a more suitable answer than “multiple values”(option B) because propositional variables are similar to variables in programming which can have only one value at a time.