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.


1