5. Determine the truth value of each of these statements if the domain for all variables consists of all integers. a) Vn(n > 0) b) 3n(n² < 0) c) an(n² = 2) d) Vn(n“ > n)

1. Given that p and q are True and r and s are False, find the truth value of the statement. (~r) = (pA(r → (~qV~s))) 2. (а) Rewrite the statements in the form of " i. x, No irrational numbers are integers. The number -4 is not equal to the square of any real number. ii. (b) Rewrite the statements in the form of "3 i. ii. x, Some exercises have answers. Some real numbers are rational. (c) Determine the truth value of the statements where D = E = {-9, –3,0,3,9}. Hence, write the negation of the statements. i. i. x in D, 3y in E such that x +y = 0. 3x in D such that Vy in E, x + y = y. 3. Find the union, intersection, and difference (A - B) of the following pairs of sets. (a) A = The set of positive odd integers less than 15. B = The set of positive even integers less than 16. (b) A = (f,l,o,w,e,r} B = {c,l, o,n, e}

For each of the following existential statements, indicate if the statementis true or false. If it is true, use a specific integer and show why it makes the statementtrue.(a) (∃n ∈ Z) (|n+5| / |n| = 2(b) (∃n ∈ Z) ((n^2 ) + 3n <0) (c) (∃n ∈ Z) (4n is odd)

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