1.

Which of the following are pairs of equal sets? E = {x : x ϵ Z, x2 ≤ 4} and F = {x : x ϵ Z, x2 = 4}.

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, 

E = {x : x ϵ Z, x2 ≤ 4}

Here, x ∈ Z and x2 ≤ 4 

If x = -2, then x2 = (-2)2 = 4 = 4 

If x = -1, then x2 = (-1)2 = 1 < 4 

If x = 0, then x2 = (0)2 = 0 < 4 

If x = 1, then x2 = (1)2 = 1 < 4 

If x = 2, then x2 = (2)2 = 4 = 4 

So, 

E = {-2, -1, 0, 1, 2} 

and F = {x : x ϵ Z, x2 = 4} 

Here, x ∈ Z and x2 = 4 

If x = -2, then x2 = (-2)2 = 4 = 4 

If x = 2, then x2 = (2)2 = 4 = 4 

So, F = {-2, 2} 

∴ E ≠ F because the elements in the both the sets are not equal.


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