Equal and Equivalent Sets - Practice Questions & MCQ

Empty Set

A set which does not contain any element in it is called the empty set (or null set or void set).

eg. A = {x: 1<x<2, x is a natural number}, 

Since no natural number lies between 1 and 2, hence A will be an empty set.

The empty set is denoted by the symbol φ or { }.

Note: φ ≠ {φ}, φ ≠ {0}

Equal Sets

Two sets A and B are said to be equal if they have exactly the same elements and we write A = B.

Otherwise, the sets are said to be unequal and we write A ≠ B.

Example  If A= {3,2,1,4} and B= {2,3,4,1}, then both have exactly same elements, and hence A = B.

Cardinal Number

The number of elements in a set is called its cardinal number. It is denoted by n(A).

If A = {a,s,d}, then n(A) = 3

and if B = {x : x² = 1}, then B = {1, -1 }, and hence n(B) = 2

Equivalent Sets

Two sets having the same number of elements are called equivalent sets.

Example: A= {H,T,P,V} and B= {1,2,3,4}, they both are equivalent as number of elements in both are same.

Equivalent sets have the same cardinal number

Note: Two equivalent sets may or may not be equal, but equal sets are always equivalent.