# CLASS-7EMPTY SET

EMPTY SET

A Set which usually does not contain any members is to be called an “Empty Set” or a “Null Set” and the empty set is denoted or implies by φ or { }

For Example –

1) The Set { x/ 5x + 4 = 0, x ϵ W } is to be considered as an empty set because,

5X + 4 = 0,

=>   5x  =  -4

=>   x = - 4/5 A.

2) The Set { x/6x + 15 = 12, x ϵ W } is to be considered as an empty set because,

6x + 15 = 12

=>  6x = 12 - 15

=>  6x = -3

=>   x = - 3/6 = - 1/2 B

Example – 1

Identify the Empty Set, Singleton Set & Pair Set

1)  A = { x / x + 5 = 4, x ϵ A }

=>  X = -5 + 4 = - 1 , -1 ϵ A and A = { -1 }, So  n(A) = 1

So, set 'A' is Singleton set.

Example – 2

Z = { x / x² + 5 = 2, x ϵ Z }

Ans.)  x² + 5 = 2 ;

x² =  2 - 5 = - 3, for any natural numbers x, So the set has no members, n(Z) = 0

Therefore set ‘Z’ is an empty set.

Example – 3

M = { x / x² + 2 = 0, x ϵ Z }

Ans.)  x² + 2 ≠ 0, for any natural number x, so the set ‘M’ has no members, n(M) =  0.

n(M) = 0, therefore ‘M’ is an empty set.

Example – 4

B = { x / x² = 25, x ϵ Y }

Ans.)  x² = 25

=>  x = 5 , 5 & - 5 ϵ Y.

So, Y = { 5, -5 } , then n (Y) = 2

So, ‘Y’ is a pair set.