Which of the following are pairs of equivalent sets?
(i) A = {–1, –2, 0} and B = { 1, 2, 3,}
(ii) C = {x : x ϵ N, x < 3} and D ={x : x ϵ W, x < 3}
(iii) E = {a, e, i, o, u} and F = {p, q, r, s, t}
(i) Equivalent Sets can have different or same elements but have the same amount of elements.
We have,
A = {–1, –2, 0} and B = {1, 2, 3,}
∴ A and B are equivalent sets because both have 3 elements in their set.
(ii) Equivalent Sets can have different or same elements but have the same amount of elements.
We have,
C = {x : x ϵ N, x < 3}
Natural numbers = 1, 2, 3, 4, …
Natural numbers less than 3 (x < 3) = 1, 2
So, C = {1, 2}
and D ={x : x ϵ W, x < 3}
Whole numbers = 0, 1, 2, 3, 4, …
Whole numbers less than 3 (x < 3) = 0, 1, 2
So, D = {0, 1, 2}
∴ C and D are not equivalent sets because their cardinality is not same.
(iii) Equivalent Sets can have different or same elements but have the same amount of elements.
We have,
E = {a, e, i, o, u} and F = {p, q, r, s, t}
∴ E and F are equivalent sets because both have 5 elements in their set.