consider the propositional functions pn n2 n 30 n 6n 5 0 rn n 0 is prime where the domain of t

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Question

Consider the propositional functions p(n): n^2 + n - 30 = (n + 6)(n - 5) = 0, and r(n): n < 0, is prime, where the domain of the variable n is the set Z of all integers. State what must hold for the quantified statement to hold and what must hold for it to be false. Determine the truth values of the quantified statement. Justify your conclusions. (You don't have to compute the truth sets of the propositional functions in order to determine the truth values. For instance, for part (a), this quantified statement is true provided that the propositional function p(n) V r(n) is true for all integers n; and is false provided that the propositional function is false for at least one integer Vn [p(n) V r(n)] 3n [p(n) v r(n)] 3n [p(n) ^ (a(n) V r(n))] Vn [p(n) ^ (a(n) ^ r(n))]

          Consider the propositional functions p(n): n^2 + n - 30 = (n + 6)(n - 5) = 0, and r(n): n < 0, is prime, where the domain of the variable n is the set Z of all integers. State what must hold for the quantified statement to hold and what must hold for it to be false. Determine the truth values of the quantified statement. Justify your conclusions. (You don't have to compute the truth sets of the propositional functions in order to determine the truth values. For instance, for part (a), this quantified statement is true provided that the propositional function p(n) V r(n) is true for all integers n; and is false provided that the propositional function is false for at least one integer Vn [p(n) V r(n)] 3n [p(n) v r(n)] 3n [p(n) ^ (a(n) V r(n))] Vn [p(n) ^ (a(n) ^ r(n))]

consider the propositional functions pn n2 n 30 n 6n 5 0 rn n 0 is prime where the domain of the variable n is the set z of all integers state what must hold for the quantified statement 67537

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