Rules of Inference Validity

Question

I'm confused in the equations. Can you help me to find this validity using rules of inference methods or resolution principle?

Answer 1

Rules used: Simplification, material equivalence, disjunctive syllogism, addition, conjunction

1 p <-> q

2 p & ~r

3 r v s.................................../(p v q) <-> s

4 p .......................................Simp 2

5 ~r ......................................Simp 2

6 s ........................................DS 3, 5

7 p v q ...................................Add 4

8 (p v q) & s ..........................Conj 6, 7

9 [(pvq) & s] v [~(pvq) & ~s] ..Add 8

10 (p v q) <-> s ......................ME 9 QED