Of all the connectives we've seen, the implication “$\rightarrow$” connective is probably the trickiest. Let $F$ and $G$ be two propositional formulas, over same set of propositional variables, such that $(F \rightarrow G)$ and $(G \rightarrow F)$ are equivalent. Which of the following is/are True?
- $(F \rightarrow G)$ is necessarily a Tautology.
- $(G \rightarrow F)$ is necessarily a Tautology.
- $(F \rightarrow G)\wedge (G \rightarrow F)$ is necessarily a Tautology.
- $F$ is necessarily equivalent to $G.$
