Which of the following are pairs of equivalent sets?(i) A = {–1, –

1.	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}
Answer» (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.

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}

Answer»

(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.