3. Show that each pair of these statements are logically equivalent by using propositional logic (use those in the Lecture 2 notes only). a) p (q + r) and q (pvr) b) (p +9)^(p+r) and p (qar) c) (pi(p vq)) and T Laws of propositional logic-Key Concepts Table 1.4.4: Laws of propositional logic. Idempotent laws: pv psp php=p Associative laws: (pvq) vrap v (vr) (219)^rap^(qar) Commutative laws: pvqqvp p^ 5^p Distributive laws: pvlqar)= (p vq)^(pvr) p^(qv) = (219) v (par) Identity laws: pvF=p pvTET PAFEF PAT=p Involution law: p = p Complement laws: pvpT TEF = F FET De Morgan's laws: (pvq) () pq = (p 9)^(9p) Conditional identities: p pva