Rewrite each statement without using quantifiers or variables. Indicate which are true and...

Rewrite each statement without using quantifiers or variables. Indicate which are true and which are false, and justify your answers as best as you can.

Exercise

Let the domain of x be the set Z of integers, and let Odd(x) be “x is odd,” Prime(x) be “x is prime,” and Square(x) be “x is a perfect square.” (An integer n is said to be a perfect square if, and only if, it equals the square of some integer. For example, 25 is a perfect square because 25 = 52.)

a. ∃x such that Prime(x)  ~Odd(x).

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b. ∀x, Prime(x) → ~Square(x).

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c. ∃x such thatOdd(x)  Square(x).