Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, is:

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] An equivalence relation containing $(1,2)$ and $(2,3)$ must link $1,2,3$ into one class: all $3	imes3=9$ pairs, plus $(4,4)$ for reflexivity, giving 10 elements. $R$ already has 3 of them, so $10-3=7$ must be added. Answer (2).

Q. Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, is:

Explanation

Reviewed by Dr. Abubacker

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