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

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}; A = {0, 1}
It can be seen that
$8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H$
$⇒ A ≠ B, A ≠ D, A ≠ E, A ≠ F, A ≠ G, A ≠ H$
Also, $2 ∈ A, 2 ∉ C$
$∴ A ≠ C$
$3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H$
$∴ B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H$
$12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H$
∴ C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H 4$$∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H
$∴ D ≠ E, D ≠ F, D ≠ G, D ≠ H$
Similarly, $E ≠ F, E ≠ G, E ≠ H$
$F ≠ G, F ≠ H, G ≠ H$
The order in which the elements of a set are listed is not significant.
∴ B = D and E = G
Hence, among the given sets, B = D and E = G.