Which of the following pairs of sets are disjoint-3- 4- 5- 6- 7 and x- x is a natural number and 7- x - 10-x- x is an odd number and x- x is an even number-x- x is a prime number and x- x is an even number-x- x is an odd number and x-x is a multiple of 3-

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Standard XII

Mathematics

Disjoint

Which of the ...

Question

Which of the following pairs of sets are disjoint?

{3, 4, 5, 6, 7} and {x: x is a natural number and 7≤ x ≤ 10}

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{x: x is a prime number} and {x: x is an even number}

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{x: x is an odd number} and {x: x is an even number}

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{x: x is an odd number} and {x:x is a multiple of 3}

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Solution

The correct option is C
{x: x is an odd number} and {x: x is an even number}

Two sets are disjoint if their intersection is a null set. Out of the given options, the option with sets {x: x is an odd number} and {x: x is an even number} have no elements in common. Thus, these sets are disjoint.

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Similar questions

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. 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. 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 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 {

c, d, e, f

}
(iii) {

x : x

is an even integer } and {

x : x

is an odd integer}

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}

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Which of the following pairs of sets are disjoint?

The correct option is C {x: x is an odd number} and {x: x is an even number} Two sets are disjoint if their intersection is a null set. Out of the given options, the option with sets {x: x is an odd number} and {x: x is an even number} have no elements in common. Thus, these sets are disjoint.

The correct option is C
{x: x is an odd number} and {x: x is an even number}

Two sets are disjoint if their intersection is a null set. Out of the given options, the option with sets {x: x is an odd number} and {x: x is an even number} have no elements in common. Thus, these sets are disjoint.