Which of the following have true value if universe of discourse consist of all integers:
A. ∃n (2n = 3n)
B. ∀n (n² ≥ n)
C. ∀n (2n > n)
D. ∃n (n² = 2)
E. ∀x∀y ∃z (xy = z)
Choose the correct answer from the options given below:

Explanation

Statement A is true since n = 0 satisfies 2n = 3n. Statement B is true because for every integer n, n² − n = n(n−1) ≥ 0 (it is non-negative for n ≤ 0 and for n ≥ 1), so n² ≥ n always holds. Statement C is false because at n = 0, 2n = 0 is not greater than n = 0 (and it also fails for negative n). Statement D is false since no integer squared equals 2. Statement E is true because the product of any two integers x and y is itself an integer, so z = xy always exists. Hence the true statements are A, B and E only.