Are \alpha and \beta logically equivalent if ~\alpha and ~\beta are?

[cristina89]

Be $\alpha$ and $\beta$ two formulas of the propositional calculus, show that $\alpha$ and $\beta$ are logically equivalent if and only if ~$\alpha$ and ~$\beta$ are logically equivalent.

 

[SW VandeCarr]

Be $\alpha$ and $\beta$ two formulas of the propositional calculus, show that $\alpha$ and $\beta$ are logically equivalent if and only if ~$\alpha$ and ~$\beta$ are logically equivalent.

Is this a homework question? If so, it should be posted in the homework section: precalculus mathematics. In any case, you need to show your attempt at a solution.

 

[HallsofIvy]

What is your definition of "logically equivalent"?