Which of the following are pairs of equal sets?G = {–1, 1} and H = {

1.	Which of the following are pairs of equal sets?G = {–1, 1} and H = {x : x ϵ Z, x2 – 1 = 0}.
Answer» Equal Sets = Two sets A and B are said to be equal if they have exactly the same elements & we write A = B We have, G = {-1, 1} and H = {x : x ϵ Z, x² – 1 = 0} Here, x ∈ Z and x² – 1 = 0 The given equation can be solved as: x² – 1 = 0 ⇒ x² = 1 ⇒ x = √1 ⇒ x = ± 1 ∴ x = -1 and 1 ∴ H = {-1, 1} ⇒ G = H because elements of both the sets are equal.

Which of the following are pairs of equal sets?G = {–1, 1} and H = {x : x ϵ Z, x2 – 1 = 0}.

Answer»

Equal Sets = Two sets A and B are said to be equal if they have exactly the same elements & we write A = B

We have,

G = {-1, 1}

and H = {x : x ϵ Z, x² – 1 = 0}

Here, x ∈ Z and x² – 1 = 0

The given equation can be solved as:

x² – 1 = 0

⇒ x² = 1

⇒ x = √1

⇒ x = ± 1

∴ x = -1 and 1

∴ H = {-1, 1}

⇒ G = H because elements of both the sets are equal.