If T(x) denotes x is a trigonometric function, P(x) denotes x is a periodic…
2017
If T(x) denotes x is a trigonometric function, P(x) denotes x is a periodic function and C(x) denotes x is a continuous function then the statement “It is not the case that some trigonometric functions are not periodic” can be logically represented as
- A.
¬∃(x) [ T(x) ⋀ ¬P(x) ]
- B.
¬∃(x) [ T(x) ⋁ ¬P(x) ]
- C.
¬∃(x) [ ¬T(x) ⋀ ¬P(x) ]
- D.
¬∃(x) [ T(x) ⋀ P(x) ]
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Correct answer: A
First, translate 'some trigonometric functions are not periodic' using existential quantification: ∃x [T(x) ∧ ¬P(x)]. Then, apply the negation 'It is not the case that' to the entire statement. This yields ¬∃x [T(x) ∧ ¬P(x)].
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