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

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.