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Tamil Nadu Board of Secondary EducationHSC Science Class 11

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence - Mathematics

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Question

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence

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Solution

Given A = {a, b, c}

R = {(a, a), (b, b), (a, c)}

After including the ordered pairs (c, c), (c, a) to R the new relation becomes

R1 = {(a, a), (b, b), (c, c), (a, c), (c, a)}

R1 is reflexive symmetric and transitive.

∴ R1 is an equivalence relation.

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Chapter 1: Sets, Relations and Functions - Exercise 1.2 [Page 18]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 1 Sets, Relations and Functions
Exercise 1.2 | Q 3. (iv) | Page 18

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