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}
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Answer 1

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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}

We know 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

It can be written as

2 ∈ A, 2 ∉ C

Therefore, A ≠ C

3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H

B ≠ C, B ≠ E, B ≠ F, B ≠ G, B ≠ H

It can be written as

12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H

Therefore, C ≠ D, C ≠ E, C ≠ F, C ≠ G, C ≠ H

4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H

Therefore, D ≠ E, D ≠ F, D ≠ G, D ≠ H

Here, E ≠ F, E ≠ G, E ≠ H

F ≠ G, F ≠ H, G ≠ H

Order in which the elements of a set are listed is not significant.

B = D and E = G

Therefore, among the given sets, B = D and E = G.

Answer 2

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)