In the relation R = {(1, 2), (2, 3)}, the minimum number of ordered pairs that…
2018
In the relation R = {(1, 2), (2, 3)}, the minimum number of ordered pairs that must be added to this set, so that the enlarged relation is reflexive, symmetric and transitive, is:
- A.
4
- B.
5
- C.
6
- D.
7
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Correct answer: D
The relation R is defined on the set {1, 2, 3}. To satisfy reflexivity, pairs (1, 1), (2, 2), and (3, 3) must be added. Symmetry requires adding the inverses (2, 1) and (3, 2). Transitivity then necessitates adding (1, 3) and (3, 1) to connect the chain. The final equivalence relation contains all 9 possible pairs on this set. Since there were originally 2 pairs, exactly 7 new pairs are required.