In the relation R={(1,2),(2,3)}, the minimum number of ordered pairs that must…
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
Answer: 7 Explanation (English): Elements = {1, 2, 3} Reflexive ⇒ add (1,1), (2,2), (3,3) → 3
Symmetric ⇒ add (2,1), (3,2) → 2
Transitive ⇒ (1,2) & (2,3) ⇒ (1,3) and (3,2) & (2,1) ⇒ (3,1) → 2 Total added = 3 + 2 + 2 = 7