Let A - x - x is an even natural number and 1- x - 12 andB - x - x is a multiple of 3- x - N and x - 12 be two sets- Find A - B- Are both sets disjoint-

A = x : x is an even natural number and 1 lt; 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, 1 ...

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Standard IX

Mathematics

Complement of a Set

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. 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)

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}

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}

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}

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}.

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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.