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Standard VI

Mathematics

Empty Set

The following...

Question

The following is an example of empty set:
${x : x$ is a natural number, $x < 8$ and simultaneously $x > 12}$ .

True

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False

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Solution

The correct option is A True
It is given that $x$ is a natural number and the condition states that $x$ is less than 8 and greater than 12 both at the same time, this is not possible as 8 is smaller than 12
Thus, the given set is an example of empty set.

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Similar questions

Which of the following are examples of empty set ?

(i) Set of all even numbers divisible by 5.

(ii) Set of all even prime numbers.

(iii) { $x : x^{2} = 0$ 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 : 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. 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 a perfect cube}

(viii)

{x : x + 5 = 8}

(ix)

{x : 2 x + 5 = 9}

(x)

{x : x \geq 7}

(xi)

{x : x ϵ N a n d 2 x + 1 > 10}

Q. 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 : 2 x + 5 = 9} (x) { x : x ≥ 7} (xi) { x : x ∈ N and 2 x + 1 > 10}

Q. Which of the following are examples of the null set (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers (iii) { x : x is a natural numbers, x < 5 and x > 7 } (iv) { y : y is a point common to any two parallel lines}

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The following is an example of empty set:{x:x is a natural number, x<8 and simultaneously x>12}.

The correct option is A TrueIt is given that x is a natural number and the condition states that x is less than 8 and greater than 12 both at the same time, this is not possible as 8 is smaller than 12Thus, the given set is an example of empty set.

The following is an example of empty set:
${x : x$ is a natural number, $x < 8$ and simultaneously $x > 12}$ .

The correct option is A True
It is given that $x$ is a natural number and the condition states that $x$ is less than 8 and greater than 12 both at the same time, this is not possible as 8 is smaller than 12
Thus, the given set is an example of empty set.