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)

Answer: B. R is symmetric and not transitive — 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:…

  1. A.

    R is reflexive and transitive

  2. B.

    R is symmetric and not transitive

  3. C.

    R is an equivalence relation

  4. D.

    R is not reflexive and not symmetric

Attempted by 124 students.

Show answer & explanation

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

A video solution is available for this question — log in and enroll to watch it.

Explore the full course: Iocl Engineers Officers Grade A Paper 2

Loading lesson…