1. (4 points) Solve the inequality 3 -4x+5 for x and write the answer using...
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1. (4 points) Solve the inequality 3 ≤ -4x+5 for x and write the answer using interval notation. 2. (6 points) Prove the following equation. Assume that b > 0, b ‡ 1, x > 0, and y > 0. Р E q 3. (5 points) Fill out the following truth table for ¬(¬r →q) ^ (¬p Vr). →→q¬¬r →q) SIF 피피 F T T T T FF T T F TF F T F F F F F F SEF T F al (a) VxP(x) (b) 3xP(x) (c) Vx-P(x) (d) -VxP(x) T T T F T F F T р r F HEHE T F T F T F T F T р q T T T T T F T F T T F F F T F T 4. (6 points) Fill out the following truth table for p → (q → r) and (p → q) → r. Are these expressions logically equivalent? why or why not? logb HEEF TFEE X Y = log₂ (x) = log₂ (y) p Vr (→ g) ^ (¬p V r) r q→ r p→ (qr) p→q (p→q) → r 5. (8 points) Let our universe be {4, 6, 8} and predicate P(x) denotes log₂ (x³) ≤ 8. Determine whether the following statements are True or False. Justify your answer. 1. (4 points) Solve the inequality 3 ≤ -4x+5 for x and write the answer using interval notation. 2. (6 points) Prove the following equation. Assume that b > 0, b ‡ 1, x > 0, and y > 0. Р E q 3. (5 points) Fill out the following truth table for ¬(¬r →q) ^ (¬p Vr). →→q¬¬r →q) SIF 피피 F T T T T FF T T F TF F T F F F F F F SEF T F al (a) VxP(x) (b) 3xP(x) (c) Vx-P(x) (d) -VxP(x) T T T F T F F T р r F HEHE T F T F T F T F T р q T T T T T F T F T T F F F T F T 4. (6 points) Fill out the following truth table for p → (q → r) and (p → q) → r. Are these expressions logically equivalent? why or why not? logb HEEF TFEE X Y = log₂ (x) = log₂ (y) p Vr (→ g) ^ (¬p V r) r q→ r p→ (qr) p→q (p→q) → r 5. (8 points) Let our universe be {4, 6, 8} and predicate P(x) denotes log₂ (x³) ≤ 8. Determine whether the following statements are True or False. Justify your answer.
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Answer rating: 100% (QA)
Lets go through each of the points one by one 1 Solve the inequality 3 leq 4x 5 for x and write the answer using interval notation First well isolate x on one side 3 5 leq 4x 2 leq 4x Now divide both ... View the full answer
Related Book For
Elementary Principles of Chemical Processes
ISBN: 978-0471720638
3rd Edition
Authors: Richard M. Felder, Ronald W. Rousseau
Posted Date:
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