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QJEEM23Ma677c: JEE Main 2023 Mathematics - Class 11 JEEM23Ma677c Solution: The minimum number of elements that must be added to the…

The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is __________.

Step-by-Step Verified Solution

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

S:{a,b,c,d}S:\{a, b, c, d\}

Adding (a,a),(b,b),(c,c),(d,d)(a, a),(b, b),(c, c),(d, d) make reflexive.

Adding (b,a),(c,b),(d,b)(b, a),(c, b),(d, b) make Symmetric

And adding (a,d),(a,c)(a, d),(a, c) to make transitive

Further (d,a)&(c,a)(d, a) \&(c, a) to be added to make Symmetricity.

Further (c,d)&(d,c)(c, d) \&(d, c) also be added.

So total 13 elements to be added to make equivalence.

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