5. Show that (– p V q) → ((p ^ ¬q) is a tautology.6. Use the laws of propositional logic to show that:a) (p V q) ^ ¬q="p ^ qb) (-p V q) → (p A q) = Pc) pA (-p→ q) = P(Note not use Truth Table)

Question 5 is wrong, two modifications possible: Either write contradiction in place of Tautology or…

Answered: 5. Show that (¬ p V q) → ((p ^ ¬q) is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q1) Evaluate whether these statements are a tautology or not: 1) (pg) → (~q"p). 2) If p and q, then r. Then, if not r, then not p or not q. 3) (p→q)V(p→~q)
7. Simplify the following using the algebra of propositions. Show your solutions. a) A = {[QV (P ^ Q)] ^ [P ^ (P ^ Q)]} b) B = {[¬(P ^ S)V ¬Q] ^ (P V ¬Q) ^ ¬(P ^ S)} c) C = [¬P → (P → Q)] → [Q → (P → P)] d) X = [(PV¬Q) A(QV¬S) ASA¬(PAQ AS)]
Determine whether each of the following is a tautology, a contradiction or neither: 19. р — (рvq) 20. (p → -q) v (-r → p) 21. (p v q) → (q v p) 22. (р q) ^ (-p v q) _23. [p → (q A r] • n)] → [(p → q) ^ (p → r)]
14. Use truth tables to establish which of the following propositional forms are tautologies, contradictions, or contingencies: a. (p^q) V[~pv (p^~q)] b. (p^~q) ^ (pVq) c. (~pvq) v (pv~q) d. (p^~p) →q 1-2) (AQ)] -4 = e. [p^ (p→q)] →q oylaqu2 Insmagus bauoibni od 101 vibiley to Yoong (ammot s 15. For the given if-then statements, find its (a) converse, (b) contrapositive, and (c) inverse. lol yil to fos@ al hond hope for numbertnauj 1(O)=((AV) 15 9)+9. (+2)+1(AADIAN] 9 a. If Jun-Jun's average in his exams is less than 75, then Jun-Jun fails. b. If it rains very hard, then the outing is cancelled. c. If Lola Tinang is getting better in her health, then she is joining the trip abroad. d. If today is Saturday, then I will jog in the Oval. e. If my computer program has no syntax errors, then it will compile. 16. Show that the proposition (p→q) →r is not logically equivalent to p→ (q→r). 0-19: S E
27. Which of the following statement is a tautology? P ∨ (P→Q) (P∨Q) →Q P ∨ (Q →P) P ∧ (~P ∨ Q)
2. Write negations of the following conditional statements: - (p→q) = p^~q (a) VneZ,ifn divisible by 2 then n is divisible by 2. (b) VxeR, if x(x+1)> 0 then x >0 or x<-1

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5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology.