Question

Choose best suited word for the following example. Let A be a family of sets and let R be the relation in A defined by 'x' is a subset of 'y'. So R is-

• A. A set
• B. A relation
• C. An equivalence relation
• D. None of the above

Answer 1

Answer: (C)

An equivalence relation

Let A be a family of sets and let R be the relation in A defined by 'x' is a subset of 'y'. So R is an equivalence relation.

Equivalence relation on set is a relation which is reflexive, symmetric and transitive.

A relation R, defined in a set A, is said to be an equivalence relation if and only if

(i) R is reflexive, that is, aRa for all a ∈ A.

(ii) R is symmetric, that is, aRb ⇒ bRa for all a, b ∈ A.

(iii) R is transitive, that is aRb and bRc ⇒ aRc for all a, b, c ∈ A.

The relation defined by “x is equal to y” in the set A of real numbers is an equivalence relation.