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 __________.
Answer (integer)
13
Solution
$R=\{(a, b)(b, c)(b, d)\}$
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$S:\{a, b, c, d\}$
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Adding $(a, a),(b, b),(c, c),(d, d)$ make reflexive.
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Adding $(b, a),(c, b),(d, b)$ make Symmetric
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And adding $(a, d),(a, c)$ to make transitive
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Further $(d, a) \&(c, a)$ to be added to make Symmetricity.
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Further $(c, d) \&(d, c)$ also be added.
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So total 13 elements to be added to make equivalence.
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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