Question

Consider the following properties:

A. Reflexive

B. Antisymmetric

C. Symmetric

Let A = {a, b, c, d, e, f, g} and R= {(a, a),(b, b),(c, d),(c, g),(d, g),(e, e),(f, f),(g, g)} be a relation on A. Which of the following property (properties) is (are) satisfied by the relation R ?

1. Only A
2. Only C
3. Both A and B
4. B and not A

Answer 1

Correct Answer - Option 4 : B and not A

The correct answer is option 4.

• If a binary relation R over a set X relates every element of X to itself, it is said to be reflexive. Since (c,c) and (d,d) is not given in the given question, it is not reflexive.
• A binary relation is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other. The given relation R is antisymmetric because for (c,d) (d,c) is not present in R. Similarly for (c,g) and (d,g).
• A binary relation is a type of binary relation. An example is the relation "is equal to", because if a=b is true then b=a is also true. Here since (c,d) is pair in a given relation R for which (d,c) is not present in it. So. it violates the Symmetric property of the relation. Hence it is not symmetric.

 ∴ Hence the correct answer is B and not-A.