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CGP EDU Academic Team
Published on: August 13, 2026
Let n be a fixed positive integer. Define a relation R on the set of integers Z, aRb ⇔ n|(a – b). Then prove that R is equivalence
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
aRb 
n|(a – b) a, b ∈ Z
n ∈ Ι +
(i) aRa 
n|(a – a) 
so R is reflexive
(ii) aRa 
n|(a – b) = n|(b – a) 
R is symmetric
(iii) aRb 
n|(a – b) and n|(b – c)
⇒ n|(a – b) + (b – c) 
n|(a – c) 
R is transitive
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