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Standard XII

Mathematics

Subset

Examine wheth...

Question

Examine whether $A =$ ${$ $x : x$ is a positive integer divisible by $3}$ is a subset of $B =$ ${$ $x : x$ is a multiple of $5$ , $x \in N$ $}$ .

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Solution

$A = {3, 6, 9, 12, 15, . . . .}$
$B = {5, 10, 15, 20.....}$
$A$ is not a subset of $B$ because $B$ does not contain all elements of $A$ .

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Similar questions

Q. Let A = {x : x ∈ N, x is a multiple of 3} and B = {x : x ∈ N and x is a multiple of 5}. Write

A \cap B

Q. State whether the following sets are finite or infinite
(i)

A =

{

x : x

is a multiple of 5,

x \in N

}
(ii)

B =

{

x : x

is an even prime number }
(iii) The set of all positive integers greater than 50.

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}

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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Examine whether A= { x:x is a positive integer divisible by 3} is a subset of B= { x:x is a multiple of 5, x∈N }.

A={3,6,9,12,15,....}B={5,10,15,20.....}A is not a subset of B because B does not contain all elements of A.

Examine whether $A =$ ${$ $x : x$ is a positive integer divisible by $3}$ is a subset of $B =$ ${$ $x : x$ is a multiple of $5$ , $x \in N$ $}$ .

$A = {3, 6, 9, 12, 15, . . . .}$
$B = {5, 10, 15, 20.....}$
$A$ is not a subset of $B$ because $B$ does not contain all elements of $A$ .