Let P denote "She is intelligent" and let Q denote "She is happy." Given below…
2025
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:
- A.
P → ¬Q; (b) P ∧ ¬Q; (c) Q → P; (d) P → ¬Q
- B.
P → Q; (b) ¬P ∧ ¬Q; (c) ¬P → Q; (d) ¬P → ¬Q
- C.
P → ¬Q; (b) ¬P ∧ ¬Q; (c) Q → P; (d) ¬P → ¬Q
- D.
P → Q; (b) P ∧ ¬Q; (c) Q → P; (d) ¬P → ¬Q
Attempted by 60 students.
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Correct answer: C
Correct translations:
a) If she is intelligent, then she is unhappy. P → ¬Q — directly matches the conditional: intelligent (P) implies not happy (¬Q).
b) She is neither intelligent nor happy. ¬P ∧ ¬Q — "neither ... nor ..." means both not P and not Q.
c) It is necessary to be not intelligent in order to be happy. Q → ¬P — "Necessary to be not intelligent in order to be happy" means if she is happy (Q) then she must be not intelligent (¬P).
d) To be not intelligent is to be unhappy. ¬P → ¬Q — "To be not intelligent is to be unhappy" expresses that not intelligent implies unhappy.
Note: None of the provided choices matches all four correct translations; the most common mistake is reversing the direction of implication in (c).
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