Let 𝐴 = {1,2,3,4,5}. Let 𝑅 be a relation on 𝐴 defined by 𝑥𝑅𝑦 if and only if 4𝑥 ≤ 5𝑦. Let 𝑚 be the number of elements in 𝑅 and 𝑛 be the minimum number of dements from 𝐴 × 𝐴 that are required to be added to 𝑅 to make it a symmetric relation. Then 𝑚 + 𝑛 is equal to:

Question

Let 𝐴 = 1,2,3,4,5. Let 𝑅 be a relation on 𝐴 defined by 𝑥𝑅𝑦 if and only if 4𝑥 ≤ 5𝑦. Let 𝑚 be the number of elements in 𝑅 and 𝑛 be the minimum number of dements from 𝐴 × 𝐴 that are required to be added to 𝑅 to make it a symmetric relation. Then 𝑚 + 𝑛 is equal to:

DivineJEE · Accepted Answer

(c): Given, 𝐴 = 1,2,3,4,5 nn𝑅 = (𝑥, 𝑦)∶ 4𝑥 ≤ 5𝑦, 𝑥, 𝑦 ∈ 𝐴 nn𝑅 = (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), nn(2,5), (3,3), (3,4), (3,5), (4,4), (4,5), (5,4), (5,5) nn∴ 𝑛(𝑅) = 16 = 𝑚 nnElements needed to make 𝑅 symmetric = (2,1), (3,1), (4,1), (5,1), (3,2), (4,2), (5,2), (4,3), (5,3) i.e., 9 elements nn∴ 𝑛 = 9 nnSo, 𝑚 + 𝑛 = 16 + 9 = 25 nn

Explanation

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