Computer Sciences > Gate 2019 > Predicate Calculus
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:
Which of the above sets satisfy φ ?
∀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
S2: Set of all positive integers
S3: Set of all integers
Which of the above sets satisfy φ ?
Correct : b
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