Which of the following statement are truth statements if universe of disclosure is set of integers :
(A) ∀n(n2 ≥ 0)
(B) ∃n(n2 = 2)
(C) ∀n(n2 ≥ n)
(D) ∃n(n2 < 0)
Choose the correct answer from the options given below:
Solution
The correct answer is (A) and (C) Only
EXPLANATION:
- (A) ∀n(n2 ≥ 0):
- This statement is true because the square of any integer is always greater than or equal to zero.
- (B) ∃n(n2 = 2):
- This statement is false. No integer squared equals 2.
- (C) ∀n(n2 ≥ n):
- This statement is true for all integers because the square of any integer is greater than or equal to the integer itself.
- (D) ∃n(n2 < 0):
- This statement is false because the square of any integer cannot be less than zero.
So, the correct option is: (A) and (C) Only.