Answer to Question #298750 in Discrete Mathematics for Snave

Question

Construct the truth table of (p \land \lnot q) \lor \lnot (q \land r) \lor (r \land p)

Use truth tables to prove that (p \land \lnot q) \lor \lnot (q \land r) \lor (r \land p) \iff p \lor \lnot q \lor \lnot r

Answer 1

Solution:

p \land \lnot q) \lor \lnot (q \land r) \lor (r \land p)

= ((p ∧ ¬q) ∨ (¬(q ∧ r) ∨ (r ∧ p)))

Truth table:

Next, p \lor \lnot q \lor \lnot r

= (p ∨ (¬q ∨ ¬r))

Its truth table:

From both the tables, we can say that their output values are same.

Thus, (p \land \lnot q) \lor \lnot (q \land r) \lor (r \land p) \iff p \lor \lnot q \lor \lnot r