Show that each pair of these statements are logically equivalent by using propositional logic (use those in the Lecture 2 notes only).

a) ( ) and ( )

b) ( ) ( ) and ( )

c) ( ( )) and T

Idempotent laws: Associative laws: Commutative laws: Distributive laws: pvp =p php=p (pvq) vrepv (vr) (P^)^rap (ar) pvqrqvp paq = q Ap pv (A)=(pvq)^(pvr) PAqvr) = (19) v (par) pvF=p PAFEF pVTET PATEP Identity laws: Involution law: p = Complement laws: pVPET TEF = F -FET De Morgan's laws (pvq) = 1^79 Conditional identities: pp va -() q P + 9 = (p) ^()