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GATE CSE 2024 Session 1 Q52: Associativity and distributivity of a ◊ b = a + 2b and a □ b = ab

Question

Consider the operators ◊\Diamond and □\Box defined by a◊b=a+2ba \Diamond b = a + 2b, a□b=aba \Box b = ab, for positive integers. Which of the following statements is/are TRUE?

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Answer: B, D (official GATE 2024 final answer key)

Concept used: Check each algebraic law by expanding both sides symbolically.

First step: Compare (a◊b)◊c=a+2b+2c(a \Diamond b) \Diamond c = a + 2b + 2c with a◊(b◊c)=a+2b+4ca \Diamond (b \Diamond c) = a + 2b + 4c, and expand a□(b◊c)a \Box (b \Diamond c).

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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