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Standard VI

Mathematics

Algebraic Expressions

Let A = x : x...

Question

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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Solution

Here A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}
A∩B = {6, 12}

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Similar questions

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}

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}

Find the intersection of each pair of sets:

(i) X = {1, 3, 5} Y = {1, 2, 3}

(ii) A = {a, e, i, o, u} B = {a, b, c}

(iii) A = {x: x is a natural number and multiple of 3}

B = {x: x is a natural number less than 6}

(iv) A = {x: x is a natural number and 1 < x ≤ 6}

B = {x: x is a natural number and 6 < x < 10}

(v) A = {1, 2, 3}, B = Φ

Q. 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?

Q. Let the universal set,

ξ

= {

x : 1 \leq x \leq 15

and x is an integer} set H = {x : x is a multiple of 3} and set K = {x : x is an even number}. Find

n (H^{'} \cap K)

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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 ∈ N and x≤12} be two sets. Find A∩B.

Here A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12} A∩B = {6, 12}

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.

Here A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}
A∩B = {6, 12}