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15. Find a useful denial (i.e., a statement logically equivalent to the negation) of each statement, and express it in mathematically precise, natural English. Express all conditional statements in the form if..., then.... Do not add implied quantifiers. (Here, a, b, c, n are fixed integers, f is a fixed function, and ro, L are fixed real numbers.)
(e) If n is a perfect square, then there exists an integer k such that n-3k or n=3k + 1. (f) be is divisible by a only if b is divisible by a or c is divisible by a 16 1. Language, Logic, and Proof () For all >0 there exists 6 > 0 such that for all x, If() - L <e if (h) For every real number M there exists a real number z such that f(x) > M. (i) If n is an odd integer, then there exists an integer k such that n = 4k+1 or n = 4k + 3.
Do e f g h i

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