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.

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

Solved Questions

Question :

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.

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