Let the relations 𝑅1 and 𝑅2 on the set 𝑋 = {1,2,3, … ,20} be given by 𝑅1 = {(𝑥, 𝑦)∶ 2𝑥 − 3𝑦 = 2} and 𝑅2 = {(𝑥, 𝑦) : −5𝑥 + 4𝑦 = 0}. If 𝑀 and 𝑁 be the minimum number of elements required to be added in 𝑅1 and 𝑅2, respectively, in order to make the relations symmetric, then 𝑀 + 𝑁 equals

Question

Let the relations 𝑅1 and 𝑅2 on the set 𝑋 = 1,2,3, … ,20 be given by 𝑅1 = (𝑥, 𝑦)∶ 2𝑥 − 3𝑦 = 2 and 𝑅2 = (𝑥, 𝑦) : −5𝑥 + 4𝑦 = 0. If 𝑀 and 𝑁 be the minimum number of elements required to be added in 𝑅1 and 𝑅2, respectively, in order to make the relations symmetric, then 𝑀 + 𝑁 equals

DivineJEE · Accepted Answer

(a) : 𝑅1 = (𝑥, 𝑦)∶ 2𝑥 − 3𝑦 = 2 𝑅1 = (4,2), (7,4), (10,6), (13,8), (16,10), (19,12) So, 6 elements are needed to make 𝑅1 symmetric ⇒ 𝑀 = 6 𝑅2 = (𝑥, 𝑦)∶ −5𝑥 + 4𝑦 = 0 𝑅2 = (4,5), (8,10), (12,15), (16,20) So, 4 elements are needed to make 𝑅2 symmetric ⇒ 𝑁 = 4 ∴ 𝑀 + 𝑁 = 6 + 4 = 10

Explanation

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