Q. 44 Consider the first order predicate formula:
∀x [( ∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w(w > x) ∧ (∀z z⏐w ⇒ ((w = z) ∨ (z = 1)))]
Here ‘a⏐b’ denotes that ‘a divides b’, where a and b are integers. Consider the following sets:
- S1: {1, 2, 3, …, 100}
- S2: Set of all positive integers
- S3: Set of all integers
Which of the above sets satisfy φ ?
(A) S1 and S3
(B) S2 and S3
(C) S1, S2 and S3
(D) S1 and S2
Answer: (B)
Explanation:
