Question:
Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.
Solution:
Given relation, R = {(a, a), (b, c), (a, b)}
To make R as reflexive we should add (b, b) and (c, c) to R. Also, to make R as transitive we should add (a, c) to R.
Hence, the minimum number of ordered pairs to be added are (b, b), (c, c) and (a, c) i.e. 3.
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