Question

From the sets given below, select equal set:
$A=\{2,4,8,12\},$

$B=\{1,2,3,4\},$

$C=\{4,8,12,14\},$

$D=\{3,1,4,2\}$

$E=\{-1,1\},$

$F=\{0,a\},$

$G=\{-1,1\},$

$H=\{0,1\}$

Answer 1

$A=\{2,4,8,12\}$
$n\left(A\right)=4$
$B=\{1,2,3,4\}$
$n\left(B\right)=4$
$C=\{4,8,12,14\}$
$n\left(C\right)=4$
$D=\{3,1,4,2\}$
$n\left(D\right)=4$
$E=\{-1,1\}$
$n\left(E\right)=2$
$F=\{0,a\}$
$n\left(F\right)=2$
$G=\{1,-1\}$
$n\left(G\right)=2$
$H=\{0,1\}$
$n\left(H\right)=2$
Number of elements in A,B,C,D are same i.e. all have $4$ elements. So ,they are comparable.
Now, we see B and D has same elements.
So, B and D are equal sets.
Similarly, E,F,G, H are comparable as they all have same number of elements i.e. $2$.
Clearly , E and G has same elements.
So, E and G are equal sets.