GATE CSE 2025 Session 2 Q15: Which predicate-logic formula is valid over the naturals
- Engineering Mathematics
- 1 mark
- MCQ
- −1/3 if wrong
Question
Let be an arbitrary predicate over the domain of natural numbers.
Which ONE of the following statements is TRUE?
Try it: multiple choice: exactly one correct option
Wrong answer costs 1/3 mark in GATE.
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Answer: A (official GATE 2025 final answer key)
Concept used: The principle of mathematical induction.
First step: Ask which hypotheses force on every natural number; for the others, build a predicate true only on some numbers (e.g. ).
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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key
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