Equal and Equivalent Sets - Practice Questions & MCQ

Empty Set

A set that 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 $\varphi$ or $\}$.
Note: $\varphi \neq\{\varphi\}, \varphi \neq\{0\}$

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 $A \neq B$.
Example If $A=\{3,2,1,4\}$ and $B=\{2,3,4,1\}$, then both have exactly the 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 $B=\left\{x: x^2=1\right\}$, 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 several 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.