Question

Which of the following two sets are equal?

• A. $A=\{1,2\}\mathrm{and}B=\left\{1\right\}$
• B. $A=\{1,2\}\mathrm{and}B=\{1,2,3\}$
• C. $A=\{1,2,3\}\mathrm{and}B=\{2,1,3\}$
• D. $A=\{1,2,4\}\mathrm{and}B=\{1,2,3\}$

Answer 1

The correct option is C

$A=\{1,2,3\}\mathrm{and}B=\{2,1,3\}$

Step 1: Explanation for the Correct option.

Two sets $A$and $B$ can be equal only if each element of set $A$ is also the element of the set $B$.

$A=\{1,2,3\}\mathrm{and}B=\{2,1,3\}$

The elements in $A$ and $B$are identical. So, these two sets are equal.

Step 2: Explanation for the incorrect options.

Option A.

$A=\{1,2\}\mathrm{and}B=\left\{1\right\}$

There are two elements in Set $A$ and one element in set $B$.

So, these two sets are not equal sets.

Option B.

$A=\{1,2\}\mathrm{and}B=\{1,2,3\}$

There are two elements in Set $A$ and three element in set $B$.

So, these two sets are not equal sets.

Option D.

$A=\{1,2,4\}\mathrm{and}B=\{1,2,3\}$

There are three elements in Set $A$ and three element in set $B$. But only two elements that is $1,2$ are common in both the sets and third element is different. So, these two sets are not equal sets.

So, these two sets are not equal sets..

Hence, option C is the correct answer.