2. Construct a valid argument: Hypotheses: Conclusion: t ~p ^ q, r⇒p, ~r⇒s,s⇒ t
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Answer Number 2
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- SOLVE STEP BY STEP IN DIGITAL FORMAT Find their truth values of the following propositions, using the laws of propositional algebra V:true F:False A A. [p→ (p ^ q)] ^ [-p → (p ^ q)] V a) (p ' q) b) (p ^ q) c) (p = q) B. [(qr) ^ (r→→q)] → (rq) a) r b) q c) r C. (rp) → [(pr) → (r^ ¬p)] a) ¬r b) p c) pWhat is the truth value of the compound proposition if p and q are true statements and r and s are false statements? (pvq) →r^[s^(rp)]? A True B FalseVII. Use truth table to prove that A ^ (B v C) = (A A B).
- 1. From a single proposition p^ (p⇒ q) Show that the q is the conclusion. 2. Construct a valid argument: Hypotheses: ~p ^ q, r⇒p, ~r⇒s, s⇒ t Conclusion: t(p O q) ^ (pO¬q) = O -g O Contradiction O p O TautologySuppose p is TRUE, q is TRUE, r is FALSE, and s is FALSE. Find the truth value of (qp) ^ (rs) TRUE FALSE
- Part 3. Use the truth table to determine whether or not each of the following is valid. 1. Q→R Q-S .. RvS 2. (G VH) →(G AH) - (GAH) ..- (GvH) 3. (I vJ) →(I^J) - (IvJ) .:- (I J)Suppose p is false, q is false, s is true. Find the truth value of (s V p) ^ (q A~s) True False2.2.4 Exercises 1. Construct the truth tables for the following compound statements: (а) р^(qVr). (b) ¬(p V (¬q)]^r. (c) (r ^p) V –¬q. (d) (р^9) V (р^г).
- (10) Let P, Q, R be mathematical statements. Consider the statement (PVQ) ⇒ (R^Q). (a) Find its contrapositive. (b) Given that this statement is false, and that is true, find all possible truth values for P, R.1. Show that the following pairs are logically equivalent: a. P^ (Q V R); (P^Q) V (P ^ R) b. P v (Q ^ R); (PVQ)^ (P V R) c. P + Q; (P → Q) ^ ( Q → P) d. P → Q; ~Q →~P ' 2. Prove the following logical implications: a. (P ^ Q) -→ Q b. (Р^@) —Р c. [(P → Q) ^P] → Q d. [(P → Q) ^ (P VR)]→(Q VR) 3. Show that the following pairs are not logically equivalent: PA -Q -P → - Q -P V - Q a. ~ (P ^ Q); b. - (P → Q); c. ~ (P V Q);B. Show that each of the following are logically equivalent. 1. p ^ (q v r) = (p ^ q) v (p ^ r). s 2. -(p A q) = -p V ¬q