Question

write the following sentences as quantified logical statements, using the universal and existential quantifiers, and defining...

write the following sentences as quantified logical statements, using the universal and existential quantifiers, and defining predicates as needed. 
Second, write the negations of each of these statements in the same way. 
Finally, choose one of these statements to prove. If it is true, prove it, and if it is false, prove its negation. Your proof need not use symbols, but can be a simple explanation in plain English. 

1. If m and n are positive integers and mn is a perfect square, then m and n are perfect squares.

2. The difference of the squares of any two consecutive integers is odd.

3. For all nonnegative real numbers a and b, sqrt(ab) = sqrt(a) * sqrt(b).
(Note that if x is a nonnegative real number, then there is a unique nonnegative real number y, denoted sqrt(x), such that y^2 = x.)

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