This is a question for discrete mathematics, A computer scientist would be anoth

Question

This is a question for discrete mathematics, A computer scientist would be another expert to solve this.

Translate the following statement into English. Let C(x) denote the propositional function "x is a cornedian" and F(x) denote "x is funny", where the domain consists of all people. Fotallx(C(x) logical F(x)). Is this a true claim? Translate thereexsits x(C(x) rightarrow F(x)). Is this true or false? What is the distinction between thereexsits x(C(x) rightarrow F(x)) and thereexsits x (C(x) logical F(x))?

Explanation / Answer

Solution:-Given that, C(x) is " x is a comedian" and F(x) such that," x is funny"

For all x, If x is a comedian then x is funny.

The statement is that every comedian is funny.

For every x, x is a comedian and x is funny,which means every person is a funny comedian.It makes no sense, because in most of the comedians some are boring comedians and some are funny comedians.

So the above statements is false, that is for every value of x,C(x) is false.

there exist a person such that if he is comedian,then he is funny.The above statement is true.because, every funny person is a comedian.

There exists lots of x, for which C(x) is false.

The English translation is that, "There exist a funny comedians", "Some funny people are comedians"

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