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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

  1. $\neg\exists x[T(x)\wedge \neg P(x)]$
     
  2. $\neg\exists x[T(x)\vee \neg P(x)]$
     
  3. $\neg\exists x[\neg T(x)\wedge \neg P(x)]$
     
  4. $\neg\exists x[T(x)\wedge P(x)]$
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Best answer
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If P is a predicate then $ \sim P $ is It is not the case that P or simply Not P

Let $P$: Some trigonometric function are not periodic, it means there exists a function which is Trigonometric and not Period

It is written as $\exists x(T(x) \land \sim P(x))$

Now It is not the case that some trigonometric function are not periodic is $\sim P$ which is written as $ \sim \exists x(T(x) \land \sim P(x))$

Hence option A) is correct

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