# Question: problem 1 for each of the following statements 1 write...

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Problem 1. For each of the following statements.

(1) Write the statement in symbolic form.

(2) Determine whether the statement is true or false. If it is false, provide a counter-example.

(3) Write the negation of the statement in symbolic form in which the negation symbol is used in front of a

conditional.

(4) Write a useful negation of the statement as an English sentence that does not use symbols as quantifers.

(a) For all integers n, if n is not a perfect square, then 2^n -1 is a prime number.

(b) For all integers n, if n is odd, then n is divisible by 7 or n is prime