Q3 of 43 Page 6

Which of the following are empty sets? Why?

i. A = {a |a is a natural number smaller than zero.}


ii. B = {x|x2 = 0}


iii. C = {x|5x – 2 = 0, x ∈ N}

i. We know that If there is not a single element in the set which satisfies the given condition then it is called a Null set or an Empty set. Empty set is represented by { }.


We know that Natural number, N = {0, 1, 2, … }.


∴ A = {a |a is a natural number smaller than zero} = {}


Ans. A is an empty set.


ii. B = {x|x2 = 0}


⇒ x2 = 0


∴ x = 0


B = {x|x2 = 0} = {0} ≠ {}


Ans. B is not an empty set.


iii. C = {x|5x – 2 = 0, x ∈ N}


⇒ 5x – 2 = 0


⇒ 5x = 2


⇒ x = 5/2


We know that natural number, N = {0, 1, 2,… }


∴ x N


∴ C = {x|5x – 2 = 0, x ∈ N} = {}


Ans. C is an empty set.


More from this chapter

All 43 →
1

Decide which of the following are equal sets and which are not? Justify your answer.

A = {x|3x – 1 = 2}


B = {x | x is a natural number but x is neither prime nor composite}


C = {x |x ∈ N, x < 2}

 2

Decide whether set A and B are equal sets. Give reason for your answer.

A = Even prime numbers


B = {x| 7x – 1 = 13}

 4

Write with reasons, which of the following sets are finite or infinite. We know that if a set is a null set or number of elements are limited and countable then it is called ‘Finite set’ and if number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.

i. A = {x|x < 10, x is a natural number}


ii. B = {y |y< -1, is an integer}


iii. C = Set of students of class 9 from your school.


iv. Set of people from your village.


v. Set of apparatus in laboratory


vi. Set of whole numbers


vii. Set of rational number

 1

If A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d} and D = {a, e}.

then which of the following statements are true and which are false?


i. C ⊆ B ii. A ⊆ D
iii. D ⊆ B iv. D ⊆ A


v. B ⊆ A vi. C ⊆ A