Question 1 Given statement variables p, q, and r, a tautology t and a contradiction c, prove the Standard Logical Equivalences highlighted in blue in the following table. pVq3qvp (p V) Vr = p V (qVr) PV (qar) = (p V9) A (PVT) p Vcep ppc Commutative laws Associative laws Distributive laws Identity laws Negation laws Double negative law Idempotent laws Universal bound laws De Morgan's laws Absorption laws Negations of t and c p1q = qap (paq) Ar = paqar) PA (Vr) = (p19) V (p Ar) pat =p pv-pet -(-p) =p pp = p pvtat ( pq) = -pv- pv (p19) =p -tec pvp = p pc = C (pvq) = -1 p () =p Et Question 3 Without using truth table, apply the laws of the standard logic equivalence to verify -(p V~qVp1-9) =~p State the law whenever it is applied. Question 4 Without using truth table, apply the laws of the standard logic equivalence to verify ~(~png) v(~p~~q)) = (p^(- (pvq))) v (png) State the law whenever it is applied. Question 5 Recalling the operator 'exclusive-or P 9 pe F T T p = (p V9) - ( pq) T F T F T T F F F a. b. Simplify pop Simplify (p pp Show that (p q r p q r) Show that (p q Ar= (p Ar) (Ar) c. d. Question 2 Use a truth table to determine if the proposition form below is a tautology or contradiction. (1-9) 1(CpVg)