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Standard XII

Mathematics

Complement

Let the unive...

Question

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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Solution

The correct option is B $5$
H' includes all numbers from 1 to 15 that are not multiples of 3.

$H^{'} \cap K = {2, 4, 8, 10, 14}$

$n (H^{'} \cap K) = 5$

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Similar questions

Q. 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)

Q. Given that the universal set,

ξ =

{x : 1 < x < 12 and x is an integer} and the sets P = {x : x is a prime number}, Q = {x : x is a multiple of 4} and R = {2, 3, 8, 9} the elements of the set

(Q \cup R)^{'} \cap P

are:

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?

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}

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Let the universal set, ξ = {x:1≤x≤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′∩K).

The correct option is B 5H' includes all numbers from 1 to 15 that are not multiples of 3.H′∩K={2,4,8,10,14}n(H′∩K)=5

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 $n (H^{'} \cap K)$ .

The correct option is B $5$
H' includes all numbers from 1 to 15 that are not multiples of 3.

$H^{'} \cap K = {2, 4, 8, 10, 14}$

$n (H^{'} \cap K) = 5$