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in Relations and Functions by (46.2k points)

In a set of natural numbers, a relation R is defined as aRb ⇔ a2 – 4ab + 3b2 = 0, (a, b ∈ N) Prove that R is reflexive but not symmetric and transitive.

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Given set N = {1, 2, 3, 4,….} 

A relation R in N is defined as 

aRb ⇔ a2 – 4ab + 3b2 = 0, ∀ a, b ∈ N

According to (i), (ii) and (iii), R is reflexive but not symmetric and transitive.

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