## EQUIVALENT AND EQUAL SETS

EQUIVALENT SETS Two finite sets A and B are equivalent only when number of elements of both the sets are equal.

Example:

A = {x : x is a natural number less than 6}

B = {x : x is a vowel of English alphabet}

n(A) = n(B) = 5

C = {2, 4, 6, 8}

D = {x : x is a letter of the word LOVE}

n(C) = n(D) = 4

Here A and B are equivalent sets.

C and D are also equivalent sets.

EQUAL SETS Two sets are equal when each elements of both sets are exactly same.

Example:

A = {1, 2, 3, 4}

B = {2, 1, 4, 3}

Here A and B are equal sets.

C = {x : x is a letter of the word ‘ALLOY’} = {a, l, o, y}

D = {x : x is a letter of the word ‘LOYAL’} = {l, o, y, a, l}

Here C and D are equal sets.

• A pair of equal sets must be equivalent, but a pair of equivalent sets may or may not be equal.

P = {1, 2, 3, 4, 5}

Q = {2, 1, 4, 5, 3}

R = {a, b, c, d, e}

S = {Monday, Tuesday, Wednesday, Thursday, Friday}

Here n(P) = n(Q) = n(R) = n(S)

P, Q, R, S are equivalent sets. P and Q are equal sets. P and Q are equivalent, but not equal.