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Standard XII

Mathematics

Empty Set

Which of the ...

Question

Which of the following sets is empty ?

A = {x : x \in W, x < 1}

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{B = x : 2 x + 1 = 2, x \in N}

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C = {x : x

is an integer and

- 2 < x \leq - 1}

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D = {

Set of months of the year beginning with letter

O}

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Solution

The correct option is B ${B = x : 2 x + 1 = 2, x \in N}$
A) set $A = {0}$
Contain one element

B) Consider set $B$
$2 x + 1 = 2$
$=> x = \frac{1}{2}$ which is not a natural number.
set B is empty

C) set $C = {- 1}$
Contain one element

D) set $D = {O c t o b e r}$
Contain one element

Hence, set $B$ is an empty set as it has no element satisfying the condition.

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Similar questions

List all the elements of the following sets :

(i) A = { $x : x^{2} < - - 10, x ϵ Z$ }

(ii) B = { $x : x = \frac{1}{2 n - 1}, 1 < - - n < - - 5$ }

(iii) { $C = x : x is an integer, - \frac{1}{2} < x < \frac{9}{2}$ }

(iv) D = {x : x is a vowel in the word "EQUATION"}

(v) E = {x : x is a month of a year not having 31 days}

(vi) F = {x : x is a letter of the word "MISSISSIPPI" }

Q. Which of the following sets :

A = {x : x i s i r r a t i o n a l a n d x^{2} - 1 = 0}

B = {x : x ϵ z a n d - 2 \leq x \leq 2}

are empty.

Q. Write the following sets in Roster form
(i)

A = {x : x \in N, 2 < X \leq 10}

(ii)

B = {x : x \in Z, - \frac{1}{2} < X < \frac{11}{2}}

(iii)

C =

{

x : x

is a prime number and a divisor of 6 }
(iv)

X =

{

x : x = 2^{n}, n \in N

and

n \leq 5

}
(v)

M = {x : x = 2 y - 1, y \leq 5, y \in W}

(vi)

P =

{

x : x

is an integer,

x^{2} \leq 16

}

Q. Let

A = [x ∶ x \in R, | x | < 1];

B = [x ∶ x \in R, | x - 1 | \geq 1]

and

A \cup B = R - D

, then the set

D

Which of the following pairs of sets are disjoint?

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 $\leq x \leq 6$ }

(ii) {a, e, i, o, u} and {b, c, d, f}

(iii) {x : x is an even integer} and {x : x is an odd integer}

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Which of the following sets is empty ?

The correct option is B {B=x:2x+1=2,x∈N}A) set A={0}Contain one elementB) Consider set B 2x+1=2=>x=12 which is not a natural number. set B is emptyC) set C={−1}Contain one elementD) set D={October}Contain one elementHence, set B is an empty set as it has no element satisfying the condition.