Let R be a non-empty relation on a collection of sets defined by A R B if and…
1996
Let R be a non-empty relation on a collection of sets defined by A R B if and only if A ∩ B = ϕ. Then, (pick the true statement)
- A.
R is reflexive and transitive
- B.
R is symmetric and not transitive
- C.
R is an equivalence relation
- D.
R is not reflexive and not symmetric
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Correct answer: B
ARB⟺A∩B=∅
Relation is defined on non-empty sets.
Reflexive:
A∩A=A≠∅A
So, R is not reflexive.
Symmetric:
If
A∩B=∅
then
B∩A=∅
So, R is symmetric.
Transitive:
Take
A={1}, B={2}, C={1}
Then,
A∩B=∅,B∩C=∅
but
A∩C={1}≠∅
So, R is not transitive.
Correct Answer: (B) R is symmetric and not transitive
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