Boolean Algebra laws of deduction question

Question

I have a question in which I'm a little stuck at answering, could anyone help?

Using the laws of deduction, show that the following statement is correct.

¬(A ∨ ¬B) ↔ B ∧ ¬A

Do I just use truth tables or is there more behind the law?

Answer 1

$¬(A ∨ ¬B)$ - Premise

$¬(B ∧ ¬A)$ - Assumption

$B$ - Assumption

$B ∧ ¬A$ - Rule of Conjunction

$⊥$ - Principle of Non-Contradiction

$¬B$ - Reductio ad Absurdum

$¬A$ - Assumption

$B ∧ ¬A$ - Rule of Conjunction

$⊥$ - Principle of Non-Contradiction

$A$ - Reductio ad Absurdum

$A ∨ ¬B$ - Rule of Addition

$⊥$ - Principle of Non-Contradiction

$B ∧ ¬A$ - Reductio ad Absurdum

De Morgan's Laws (Logic)/Disjunction of Negations/Formulation 1/Reverse Implication

Definition:Natural Deduction