Question

From the sets given below, select equal sets:
$A=\{2,4,8,12\},B=\{1,2,3,4\},C=\{4,8,12,14\},D=\{3,1,4,2\}$
$E=\{-1,1\},F=\{0,a\},G=\{1,-1\},H=\{0,1\}$

Answer 1

Given
$A=\{2,4,8,12\},B=\{1,2,3,4\},C=\{4,8,12,14\},D=\{3,1,4,2\}$
$E=\{-1,1\},F=\{0,a\},G=\{1,-1\},H=\{0,1\}$

Step $1:$ Compare set $A$ with others sets.
Here we can clearly observe that all the elements of set $A$ are present in none of the other sets. So, it is equal to none of the sets mentioned above.

Step $2:$ Compare set $B$ with others sets.
Here we can observe that all the elements of set $B$ are present in set $D$ and every element of set $D$ is present in set $B.$
So, $B=D$

Step $3:$ Compare set $C$ with others sets.
Here we can clearly observe that all the elements of set $C$ are present in none of the other sets. So, it is equal to none of the sets mentioned above.

Step $4:$ Compare set $E$ with other sets
Here we can observe that all the elements of set $E$ are present in set $G$ and every element of set $G$ is present in set $E.$
So, $E=G$

Step $5:$ Compare set $F$ with other sets
Here we can clearly observe that all the elements of set $F$ are present in none of the other sets. So, it is equal to none of the sets mentioned above.

Step $6:$ Compare set $H$ with other sets
Here we can clearly observe that all the elements of set $H$ are present in none of the other sets. So, it is equal to none of the sets mentioned above.

Final Answer: $B=D$ and $E=G$