How do I prove this logical equivalence?

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$\phi$ is a well formed formula.

f($\phi$) is given by replacing ∧ with ∨ (and vice versa) and 1 with 0 (and vice versa) in $\phi$.

g(f($\phi$)) is given by replacing all literals in f($\phi$) (obtained above) with their negations.

For all $\phi$, prove that g(f(¬ $\phi$)) is logically equivalent to $\phi$.

From what I know, there are two ways to prove this - using truth tables, or by proving that $\phi$ ↔ g(f(¬ $\phi$)). But I find the question too vague/abstract, and I am unable to solve it using either method.

Please help.