Question

State whether the following pair of sets are equivalent but not equal.

$\text{A =}\left\{\text{letters in the word DELHI}\right\}\text{, B =}\left\{\text{letters in the word BOMBAY}\right\}$

Answer 1

Step $\mathbf{1}$: Definitions:

Equal sets: Two sets are said to be equal if they have the same elements. All equal sets have an equal number of elements. But all sets having an equal number of elements may or may not be equal.

Equivalent sets: Two sets are said to be equivalent if the number of elements in both sets are equal. All equal sets are equivalent but equivalent sets may or may not be equal.

Step $\mathbf{2}$: Solution:

Here,

$$\begin{gathered} \text{A =}\left\{\text{letters in the word DELHI}\right\} \\ \text{=}\left\{D,E,L,H,I\right\} \end{gathered}$$

and

$$\begin{gathered} \text{B =}\left\{\text{letters in the word BOMBAY}\right\} \\ \text{=}\left\{B,O,M,A,Y\right\} \end{gathered}$$

Here, a number of elements in the set $\mathrm{A}$ $=5$ and the number of elements in the set$\mathrm{B}$$=5$.

As the numbers of elements are the same but the elements are different.

So, the set $\mathrm{A}$and set $\mathrm{B}$ are equivalent but not equal.

Hence, the given pair of sets are equivalent but not equal.