Let A = p ↔ [q ^ (~ r -> p)].

Question

(a)Construct a truth table for the expression A. Hence determine whether the

expression A is a tautology, contradiction, or contingency.

(b) Obtain the Principal Disjunctive Normal Form (PDNF) and Principal

Conjunctive Normal Form (PCNF) of A. Hence, deduce the PDNF and PCNF

of ~A.

Answer 1

p q r ~r ~r->p q ^ (~r->p) ---> <---- A

T T T F T T T T T

T T F T T T T T T

T F T F T F F T F

T F F T T F F T F

F T T F T T T F F

F T F T F F T T T

F F T F T F T T T

F F F T F F T T T

Karnaugh Map

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r

--

pq 0 1

00 1 1

01 0 0

10 0 1

11 1 1

p q + ~r