# CHECK IF THE GIVEN SETS ARE EQUAL AND EQUIVALENT

## About "Check if the Given Sets are Equal and Equivalent"

Check if the Given Sets are Equal and Equivalent :

Here we are going to see how to find the cardinal number of a set.

## Equal and Equivalent Sets

Equal sets :

Two sets are said to be equal if they contain exactly the same elements, otherwise they are said to be unequal.

In other words, two sets A and B are said to be equal, if

(i) every element of A is also an element of B

(ii) every element of B is also an element of A

Equivalent Sets :

Two finite sets A and B are said to be equivalent if

they contain the same number of elements. It is written as A ≈ B.

If A and B are equivalent sets, then n(A) = n(B)

## Check if the Given Sets are Equal and Equivalent - Practice Problems

Question 1 :

Which of the following sets are equivalent or unequal or equal sets?

(i) A = The set of vowels in the English alphabets.

B = The set of all letters in the word “VOWEL”

Solution :

A  =  {a, e, i o, u}

B  =  {V, O, W, E, L}

n(A)  =  5, n(B)  =  5

Since n(A)  =  n(B), they are equivalent sets.

(ii) C = {2, 3, 4, 5}

D = { x : x ∈ W, 1 < x < 5}

Solution :

D = {2, 3, 4}

The number of elements are not same and set D contain 1 lesser element than C. Hence they are unequal sets.

(iii) E = The set of A={ x : x is a letter in the word “LIFE”}

F = {F, I, L, E}

Solution :

E  =  { L, I, F, E }

= {F, I, L, E}

In both sets we have same elements. Hence they are equal sets.

(iv) G = {x : x is a prime number and 3 < x < 23}

H = {x : x is a divisor of 18}

Solution :

G = {5, 7, 11, 13, 17, 19} and n(G)  =  6

H = {1, 2, 3, 6, 9, 18} and n(H)  =  6

Since the number of elements of both sets are same. They are equivalent sets.

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