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GATE CSE 2025 Session 1 Q24: Identities of the 3-input majority function

Question

Let XX be a 3-variable Boolean function that produces output as '1' when at least two of the input variables are '1'. Which of the following statement(s) is/are CORRECT, where a,b,c,d,ea, b, c, d, e are Boolean variables?

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Answer: B, D (official GATE 2025 final answer key)

Concept used: Majority function properties: X(a,a,z)=aX(a, a, z) = a and X(a,b,z)X(a, b, z) equals aa when a=ba = b.

First step: Simplify inner terms first: X(a,b,a)=aX(a, b, a) = a, X(a,c,c)=cX(a, c, c) = c; then split into the cases a=ba = b and a≠ba \ne b.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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