Which of the following are pairs of equivalent sets?

Question:

Which of the following are pairs of equivalent sets?

(i) $A=\{-1,-2,0\}$ and $B=\{1,2,3,$,

(ii) $C=\{x: x \in N, x<3\}$ and $D=\{x: x \in W, x<3\}$

(iii) $E=\{a, e, i, o, u\}$ and $F=\{p, q, r, s, t\}$

 

Solution:

 (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,

$\mathrm{C}=\{\mathrm{x}: \mathrm{x} \in \mathrm{N}, \mathrm{x}<3\}$

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. 

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