ISRO-DEC2017-7

Question

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. $\neg\exists x[T(x)\wedge \neg P(x)]$
   
• B. $\neg\exists x[T(x)\vee \neg P(x)]$
   
• C. $\neg\exists x[\neg T(x)\wedge \neg P(x)]$
   
• D. $\neg\exists x[T(x)\wedge P(x)]$

Answer 1

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