| Q. Consider the first order predicate formula 𝜑: ∀𝑥 [(∀𝑧 𝑧|𝑥 ⇒ ((𝑧 = 𝑥) ∨ (𝑧 = 1))) ⇒ ∃𝑤 (𝑤 > 𝑥) 𝖠 (∀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 S2 | (B) S1 and S3 | (C) S2 and S3 | (D) S1, S2 and S3 |
Solution:
