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Question 3 (a) Let p,q,r and s be four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pA-g) -→ (q Ar)) → (s V ¬q) ii. ((p V q) A (q V s)) → ((-r V p) ^ (q V s)) (b) Let p,q and r be three propositions defined as follows: p means ' Sofia is happy ', q means 'Sofia paints a picture ' whereas r means ' Samir is happy Express each of the three following compound propositions symbolically by using p, q and r, and appropriate logical symbols. i. '" Sofia is happy and paints a picture then Samir isn't happy ii. 'Sofia is happy only if she paints a picture ii. 'Sofia either paints a picture or she is not happy (c) Give the contrapositive, the converse and the inverse of each of the followin statement: i. Vr E R, if > 3 then r> 9 ii. Vr ER. if r(r+ 1) >0 then r > 0 or r< -1 (d) A tautology is a proposition that is always true. Let p.y and r be three propositions, show that (p iy Vr) (tpA 4) -r) is a tautology.

Question 3 (a) Let p,q,r and s be four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pA-g) -→ (q Ar)) → (s V ¬q) ii. ((p V q) A (q V s)) → ((-r V p) ^ (q V s)) (b) Let p,q and r be three propositions defined as follows: p means ' Sofia is happy ', q means 'Sofia paints a picture ' whereas r means ' Samir is happy Express each of the three following compound propositions symbolically by using p, q and r, and appropriate logical symbols. i. '" Sofia is happy and paints a picture then Samir isn't happy ii. 'Sofia is happy only if she paints a picture ii. 'Sofia either paints a picture or she is not happy (c) Give the contrapositive, the converse and the inverse of each of the followin statement: i. Vr E R, if > 3 then r> 9 ii. Vr ER. if r(r+ 1) >0 then r > 0 or r< -1 (d) A tautology is a proposition that is always true. Let p.y and r be three propositions, show that (p iy Vr) (tpA 4) -r) is a tautology.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question 3 (a) Let p,q,r and s be four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pA-a) → (g Ar)) → (s V ¬q) i. ((p V q) ^ (q V s)) → ((¬r V p) ^ (q V ) (b) Let p, q and r be three propositions defined as follows: p means ' Sofia is happy', q means 'Sofia paints a picture ' whereas r means ' Samir is happy Express each of the three following compound propositions symbolically by using p,q and r, and appropriate logical symbols. i. If Sofia is happy and paints a picture then Samir isn't happy ii. 'Sofia is happy only if she paints a picture i. "Sofia either paints a picture or she is not happy (c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vr E R, if a > 3 then > 9 ii. Vr ER. if r(r + 1) > 0 then r > 0 or r < -1 (d) A tautology is a proposition that is always true. Let p.y and r be three propositions, show that (piVr) (tpA-) r) is a tautology.
Transcribed Image Text:Question 3 (a) Let p,q,r and s be four propositions. Assuming that p and r are false and that q and s are true, find the truth value of each of the following propositions: i. ((pA-a) → (g Ar)) → (s V ¬q) i. ((p V q) ^ (q V s)) → ((¬r V p) ^ (q V ) (b) Let p, q and r be three propositions defined as follows: p means ' Sofia is happy', q means 'Sofia paints a picture ' whereas r means ' Samir is happy Express each of the three following compound propositions symbolically by using p,q and r, and appropriate logical symbols. i. If Sofia is happy and paints a picture then Samir isn't happy ii. 'Sofia is happy only if she paints a picture i. "Sofia either paints a picture or she is not happy (c) Give the contrapositive, the converse and the inverse of each of the following statement: i. Vr E R, if a > 3 then > 9 ii. Vr ER. if r(r + 1) > 0 then r > 0 or r < -1 (d) A tautology is a proposition that is always true. Let p.y and r be three propositions, show that (piVr) (tpA-) r) is a tautology.
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