B, Determine if the following compoundpropositions is a TAUTOLOGY,CONTRADICTION, or CONTINGENCY1. PV(р^а)2. р — (рVф)P -→ (p V q)3. (р — 9) — (~pVq)→(~pV q)

Answered: Image /qna-images/answer/107ed31a-bbe6-4d4a-b49b-11de48e0c030.jpg

Answered: B, Determine if the following compound…

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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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)
6. Match each logical statement in the left hand column with an equivalent logical statement in the right hand column. Logical Statement (i) ~ WA~y Logical Statement (v) w v ~y (ii) wA~y (vi) ~ (~w→ y) (iii) w v y (vii) ~ (~w v y) (viii) ~ w → y (iv) ~ (~WAy)
6 5. (a) Decide about the truth values of the statement form up the following truth table. - (pV ~ q) ^ (p V q) by filling T F F T F F (b) Is the statement form given in part (a) logically equivalent to (~ p) ^ q? Support your answer.
IV. Simplify the given propositions using Rules of Logical Equivalences. Do not forget to indicate the rule/s applied for each step. 1. (-р^т) (р^а) 2. (q → ¬p) V (p → q) 3. p ^ (q → ¬r) A ((r → p) V (¬p ^ q ^ ¬r))
2. Determine whether the given formula is a tautology (T), a contradiction (C), or a synthetic one(S) in predicate logic. ~(Vy3x D(y,x) →3xVy D(y,x)) (D(y,x): y admires x )
(by d) Construct a truth table and identify any Tautology. с. Q.2) . [ (r ^p) A (p A q)] →p b. r> (p^~q)
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
Write the negation of the propositions symbolically
16. Complete the truth table for the given statement by filling in the required columns. (e v f) e f e vf ~(e V f) тт T F F T F F Complete the truth table. e vf ~(e v f) (1) (2) (3) (4) T F (5) (6) F T. (7) (8) F (1) O F От (5) O F OT (7) O F От (2) O F (3) O T O F (4) O T O F (6) O T O F (8) O F От
D. Determine the truth value of each proposition, given that p and q are true propositions and r and s are false propositions. Show your solution. (4 points) 1. [[(p → r)^(q → r)] → [(sVq)/^~r]] → s 2. -(~qAp) → [(p → ~s) → ~r] 3. [(pVp) → ~r]^~[(s → ~q)^~p] 4. (p + ~q) –→r + [[p → ~s) +→ ~r]
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 .

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B, Determine if the following compound propositions is a TAUTOLOGY, CONTRADICTION, or CONTINGENCY 1. PV ~ (p^q) 2. Р — (рVq) P - → (p V q) (p → q) → (~ p V q) 3.