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Standard XII

Mathematics

Signum Function

Let A = x : x...

Question

Let A = {x : x is an even natural number and 1< x $\leq$ 12} and
B = { x : x is a multiple of 3, x $ϵ$ N and x $\leq$ 12} be two sets. Find A $\cap$ B. Are both sets disjoint?

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Solution

A = {x : x is an even natural number and 1< x $\leq$ 12} = {2, 4, 6, 8, 10, 12} B = { x : x is a multiple of 3, x $ϵ$ N and x $\leq$ 12} = {3, 6, 9, 12}

A $\cap$ B = {2, 4, 6, 8, 10, 12} $\cap$ {3, 6, 9, 12}

A $\cap$ B = {6, 12}

No, the given sets are not disjoint sets.

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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. 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. 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}

Q. Let A = {x : x is an even natural number and 1< x ≤ 12} and
B = { x : x is a multiple of 3, x ∈ N and x≤12} be two sets. Find A∩B.

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Let A = {x : x is an even natural number and 1< x ≤ 12} and B = { x : x is a multiple of 3, x ϵ N and x ≤ 12} be two sets. Find A ∩ B. Are both sets disjoint?

A = {x : x is an even natural number and 1< x ≤ 12} = {2, 4, 6, 8, 10, 12} B = { x : x is a multiple of 3, x ϵ N and x ≤ 12} = {3, 6, 9, 12} A ∩ B = {2, 4, 6, 8, 10, 12}∩ {3, 6, 9, 12} A ∩ B = {6, 12} No, the given sets are not disjoint sets.

Let A = {x : x is an even natural number and 1< x $\leq$ 12} and
B = { x : x is a multiple of 3, x $ϵ$ N and x $\leq$ 12} be two sets. Find A $\cap$ B. Are both sets disjoint?

A = {x : x is an even natural number and 1< x $\leq$ 12} = {2, 4, 6, 8, 10, 12} B = { x : x is a multiple of 3, x $ϵ$ N and x $\leq$ 12} = {3, 6, 9, 12}

A $\cap$ B = {2, 4, 6, 8, 10, 12} $\cap$ {3, 6, 9, 12}

A $\cap$ B = {6, 12}

No, the given sets are not disjoint sets.