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Relations and Functions
Xam Idea
CBSE
Grade 12
Question:
Let $R$ be a relation on $\mathbb{N} \times \mathbb{N}$ defined by $(a, b) R (c, d) \iff a + d = b + c$. Show that $R$ is an equivalence relation. Find equivalence class $[(2, 5)]$.
Step-by-Step Solution
Key Concept: Reflexive: a+b=b+a. Symmetric: c+b=d+a. Transitive: sum of equations. Class [(2,5)] = {(x,y) : y - x = 3}.
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Correct Answer:
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