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Standard VIII

Mathematics

Empty Set

Which of the ...

Question

Which of the following is not a null set?

A = {x: -10<x<2, x is a natural number}

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B = {x:x is an even prime number greater than 2}

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C = {x: x²- 3=0, x is rational number}

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D = {x: x is an odd natural number divisible by 2}

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Solution

The correct option is A
A = {x: -10<x<2, x is a natural number}

A = {1}, 1 is the only natural number between -10 and 2

B = { }; 2 is the only even prime. There are no numbers greater than 2 that are even prime.

C = { }; $x^{2}$ - 3=0⇒x=± $\sqrt{3}$ which is irrational.

D = { }; odd numbers are not divisible by 2.

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Similar questions

Q. 7.If A= {x : x is a natural number }, B = {x : x is an even natural number)C= {x:x is an odd natural number) andD = {x : x is a prime number ], find) An B(iv) BC(ii) AnID(vi) Cn Di) AnC

Q. Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by 5;
(ii) Set of all even prime numbers;
(iii) {x : x² −2 = 0 and x is rational};
(iv) {x : x is a natural number, x < 8 and simultaneously x > 12};
(v) {x : x is a point common to any two parallel lines}.

Q. Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by

5

(ii) Set of all even prime numbers.
(iii)

{x : x^{2} - 2 = 0

and

x

is rational

}

(iv)

{x : x

is a natural number,

x < 8

and simultaneously

x > 12

(v)

{x : x

is a point common to any two parallel lines

}

Taking the set of natural numbers as the universal set, write down the complement of the following sets :

(i) {x : x is an even natural number}

(ii) {x : x is an odd natural number}

(iii) {x : x is a positive multiple of 3}

(iv) {x : x is a prime number}

(v) {x : x is a natural number divisible by 3 and 5}

(vi) {x : x is a perfect square}

(vii) {x : x is a perfect cube}

(viii) {x : x + 5 = 8}

(ix) {x : 2x + 5 = 9}

(x) {x : x $\geq$ 7}

(xi) {x : x $\in$ N and 2x + 1 > 10}

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {x: x is an even natural number}

(ii) {x: x is an odd natural number}

(iii) {x: x is a positive multiple of 3}

(iv) {x: x is a prime number}

(v) {x: x is a natural number divisible by 3 and 5}

(vi) {x: x is a perfect square}

(vii) {x: x is perfect cube}

(viii) {x: x + 5 = 8}

(ix) {x: 2x + 5 = 9}

(x) {x: x ≥ 7}

(xi) {x: x ∈ N and 2x + 1 > 10}

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