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}.
As, Two set A and B are said to be equal if they have exactly same elements then we say A = B.
As we see, 8 belongs to A, but 8 does not belong to B,D,E,F,G and H.
⇒ A≠B, A≠D, A≠E, A≠F, A≠G, A≠H.

And 2 belongs to A but 2 does not belong to C
⇒ A≠C.

Now, 3 belongs to B, but 3 does not belong to C,E,F,G and H.
⇒ B≠C, B≠E, B≠F, B≠G, B≠H

Also, 12 belongs to C, but 12 does not belong to D,E,F,G and H.
⇒ C≠D, C≠E, C≠F, C≠G, C≠H

Also, 4 belongs to D, but 4 does not belong to E,F,G and H.
⇒ D≠E, D≠F, D≠G, D≠H

Also, -1 belongs to E, but -1 does not belong to F,G and H.
⇒ E≠F, E≠G, E≠H

Also, a belongs to F, but a does not belong to G and H.
⇒F≠G, F≠H

Also, -1 Є G, but -1 does not belong to H
⇒ G≠H

Because elements of set (B and D) and (E and G) do not have significant order but (B and D) and (E and G) have same element.
∴ B = D and E = G.

hence, equal sets are (B , D) and (E , G)