Which of the following are pairs of equal sets?

G = {–1, 1} and H = {x : x ϵ Z, x2 – 1 = 0}.


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.


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