Computer Sciences > GATE 2025 SET-2 > Mathematical Logic

Contributed by: Dr. Sarah Chen

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Let P(x) be an arbitrary predicate over the domain of natural numbers.
Which ONE of the following statements is TRUE?

A

(P(0)&land;(∀x[P(x)⇒P(x+1)]))⇒(∀x P(x))

B

(P(0)&land;(∀x[P(x)⇒P(x-1)]))⇒(∀x P(x))

C

(P(1000)&land;(∀x[P(x)⇒P(x-1)]))⇒(∀x P(x))

D

(P(1000)&land;(∀x[P(x)⇒P(x+1)]))⇒(∀x P(x))

Check Answer

Explanation

Correct : a

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