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Question: definition 1 an integer n is a perfect square provided...

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Definition 1. An integer n is a perfect square provided that the exists a non-negative k such that deinition can be written in symbolic form using appropriate quantifiers as follows n . This An integer n is a perfect square provided (3k E No)n-k) Examples: 11,22,9 3, 16-4... are perfect squares. finition 2. A positive integer n greater than 1 is prime if its only positive factors are 1 and itself For the universe of all ategers, let ole), D, Pa, and ste) be the folowing eanterc O(x) :z is odd D(r) : z is divisible by7 P(r) : a is prime S(x) :a is a perfect square Problem 2. For each of the following statements. (1) Write the statment in symbolie 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 symbolie form in which the negation symbol is used in front of a conditional tion of the statement as an English sentence that does not use symbols as quantifiers (a) For all integers m and n, if m and n are perfect squares, then n - m is even. (b) There exists an integer m such that m + n is even for all integers nn.

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