3. Consider the following propositions:P→ 9,g^-p.-P→→q,-pv q,9 → P.-q V p,q→P.р^-4.(a) Which proposition is the converse of p → q?(b) Which proposition is the contrapositive of pq?(c) Which propositions are logically equivalent toP→q?

Answered: Image /qna-images/answer/23c53792-b1f9-4928-8207-1409b456790e.jpg

Answered: 3. Consider the following propositions:…

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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Let p, q and r be the propositions, p: Today is my birthday. q: I want to eat cake. r: I want to have a present. (a) Express each of these compound propositions as an English sentence. (-qv~r)+> p (i) (ii) p¬(q^r)
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Let p and q be two propositions. Consider the following two statements in prepositional logic. S₁: (-p^(pv q)) → p S₂: q→(-p^ (pvq)) Which of them is tautology
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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
3. (a) Let p and q be two logical propositions. Give the truth table for the two compound propositions and p^ (q V ¬p), and decide whether they are equivalent or not. (b) Give the contrapositive of the following statement concerning positive integers n,a and b: If n ab then a < Vn or b < n. (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b < Vn. such that n =
Activity 5. Propositions and Logical Operators A. Given the following propositions: P: Cecilion studied hard for his math exam. Q: Cecilion got a high score on his math exam. Write each of the following propositions as an English sentence. 1-2. P V Q ~P^Q 3-4. ~Q → ~P 5-6. ~P 9-10. 7-8. P+ Q B. Determine whether each of the following is a proposition or not a proposition. Write P if it's a propo and MS, otherwise. 14. Today is awesome! 15. She is beautiful. U 11. 2x + 4 > 6 when x = 5. %3D 12. Baguio is the summer capital of the Philippines. M 13. 11x + 2 = 5.
TASK 1: Express the following propositions in symbols, where p,r and s are as follow: p: Neil is a big eater q: Len has a big voice r: Jeric likes to travel s: Leny likes violet 1. It is not true that Neil is a big eater and Leny does not like violet. 2. It may or may not be the case that Leny likes violet . 3. Either Neil is a big eater or Len has a big voice, yet Leny likes violet 4. If Neil is a big eater or Len has a big voice, then Leny likes violet 5. Neil is a big eater or Len has a big voice if and only if Leny like Violet and Jeric likes to travel .
Match each of the following compound propositions with the logically equivalent one. (pV¬q) P→→q (p → a) (p^(-(p^ q))) 1. ¬p/q 2. p V q 3. pVq 4. p -q

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3. Consider the following propositions: P→ 9. g^-P. -P→→q, -pvq, 9 → P. -q V p. -9→P. P^-4. (a) Which proposition is the converse of p → q? (b) Which proposition is the contrapositive of p→q? (c) Which propositions are logically equivalent to P→q?