GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 2

Answer 1

A tautology is a formula that will evaluate to true under every truth value assignment.

First, eliminate the obvious candidates $p, p \vee p$, and $\neg \neg$ are all false when $p$ is false.

Now, notice that $(p \rightarrow q) \wedge(q \rightarrow p)$ is the same as $(p \leftrightarrow q)$ which will be false whenever the values of $p$ and $\mathrm{q}$ are different.

Hence the only option left is $p \rightarrow(q \rightarrow p)$. Can confirm that this is a tautology by building a truth table and verifying that it is true for all rows.