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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Ex 1.1, 9 Show that each of the relation R in the set A = {x ∈ Z: 0 ≤ x ≤ 12} , given by (ii) R = {(a, b): a = b} is an equivalence relation. Find the set of all elements related to 1 in each case. A = {x ∈ Z: 0 ≤ x ≤ 12} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} R = {(a, b) : a = b} Check reflexive Since a = a is always true, So, (a, a) ∈ R, ∴ R is reflexive. Check symmetric We know that If a = b, then b = a Hence, if (a, b) ∈ R, then (b, a) ∈ R Hence, R is symmetric Check transitive If a = b & b = c, then a = c If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R Hence, R is transitive Hence, R is reflexive, symmetric and transitive, ∴ it is equivalence relation We need to find set of elements related to 1 R = {(a, b) : a = b} All elements related to 1 means a = 1, If a = 1, then b = a = 1 ∴ Only (1, 1) satisfies the relation. Hence, the set of elements related to 1 is {1}.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.