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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”
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Solution
Reflexivity:
aRa ∀a ∈ A
“Is a not a sister of herself?”
Nobody is a sister of herself.
Every element is related to itself.
R is reflexive.
Symmetry:
aRb ⟹ bRa
if a is not a sister of b, then b is not a sister of a.
True, because “sisterhood” is a mutual relation.
If A is not sister of B, then B is not sister of A.
R is symmetric.
Transitivity:
aRb and bRc ⟹ aRc
If a is not a sister of b, and b is not a sister of c, must it follow that a is not a sister of c?
R is not transitive.
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