Let P denote "She is intelligent" and let Q denote "She is happy." Given below are the statements:
(a) If she is intelligent, then she is unhappy.
(b) She is neither intelligent nor happy.
(c) It is necessary to be not intelligent in order to be happy.
(d) To be not intelligent is to be unhappy.
Which of the following is the correct propositional expression for the above statements?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: C. (a) P → ¬Q; (b) ¬P ∧ ¬Q; (c) Q → ¬P; (d) ¬P → ¬Q
Explanation
(a) is P → ¬Q. 'Neither P nor Q' is ¬P ∧ ¬Q. 'X is necessary for Y' means Y → X, so (c) is Q → ¬P. 'To be not intelligent is to be unhappy' means ¬P → ¬Q.More Discrete Structures and Optimization questions
- In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both Rice and bread, 25 eat both Rice and curd, 15 eat both bread…
- Choose the correct statement for a group G:
- Let m and n be positive integers. Consider: (A) If n ≠ 1, then m < mn. (B) If k is composite, then k = mn where 1 < m, n > k. (C) If mn = 1…
- Which one of the following is NOT a basic solution of the system of linear equations x₁ + 2x₂ + x₃ = 4 2x₁ + x₂ + 5x₃ = 5
- Match List I with List II: match the logically equivalent propositionsList I List II A. p → q I. (p ∧ q) ∨ (¬p ∧ ¬q) B. ¬(p ∨ (¬p ∧ q)) II.…
- The probability that A hits a target is 1/4, and the probability that B hits the target is 2/5. Both shoot at the target. What is the proba…