Question: Solve with explanation.. *c. AVB, ~AV~B /. . ~(A = B) d. A = ~ (B VC), B = (D . ~ E), ~ (E

Solve with explanation..

*c. AVB, ~AV~B /. . ~(A = B) d. A = ~ (B VC), B = (D . ~ E), ~ (E . A) / .. A ~D SUMMARY OF RULES OF INFERENCE Modus Ponens (M.P.) Modus Tollens (M.T.) Hypothetical Syllogism (H. S.) P-q p>q p q 1:.q 1:.~P Simplification (Simp.) Conjunction (Conj.) Dilemma (Dil.) P . q P . q P p- q 1.. P 1:. 9 q r Ds 1..P . q pur A. Conditional Proof (C.P.) 19VS Disjunctive Syllogism (D. S.) Addition (Add.) pvq pv q P 1:. pvq 1:. pvq 1.. 9 1.. P p Pq SUMMARY OF REPLACEMENT RULES B. Indirect Proof (I.P.) Double Negation (D.N.) Duplication (Dup.) pi: ~ ~p P :: (PVP) p : (p . p) Commutation (Comm.) Association (Assoc.) (pv q) :: (q vp) (pvq) vr) :: (pv(qvr)) ~ p (p . q) :: (9 .P) ((p . q) . r) :: (p . (q. r)) Contraposition (Contrap.) DeMorgan's (DeM.) (p > q) :: (~q> ~P) ~ (pv q) :: (~p . ~q ~(p . q) :: (~pv ~q) Biconditional Exchange (B.E.) Conditional Exchange (C.E.) (p = q) :: ((p > q) . (9>p)) (p > q) :: (~pv q) Distribution (Dist.) Exportation (Exp.) (p . (qvr)) :: ((p . q) v(p .r)) ((p . q) > r) :: (p>(9>r)) (pv (q . r)) :: ((pvq) . (pvr)) Please solve the two proofs using only the rules above

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