**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 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)

**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 = {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.

After having gone through the stuff given above, we hope that the students would have understood, "Check if the Given Sets are Equal and Equivalent".

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