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Question
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the female members of a family. The relation R defined by “aRb if a is not a sister of b”
Solution
A = {set of all female members of a family}
(a) aRa ⇒ a is a sister of a
It is reflexive
(b) aRb ⇒ a is a sister of b
bRa ⇒ b is a sister of a
⇒ It is symmetric
(c) aRb ⇒ a is a sister of b
bRc ⇒ b is a sister of c
aRc ⇒ a can be sister of c
It is not transitive.
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