Question

3. Let A= {x: X is a prime number less than 11} and
B = {x: x is an integer such that 2 =< x <= 8}
a) Write C =A n B.
b)Find the number of subsets of C which has 3 elements.​

Answer 1

First question :

Given ,

A= {x : x is a prime number less than 11}

it can be written as ,

A = { 2 , 3 , 5 , 7 , }

and

B = {x : x is an integer such that 2 =< x <= 8}

it can be written as ,

B = { 2 , 3 , 4 , 5 , 6 , 7 , 8 }

Thus ,

$\sf \mapsto A \cap B = \{ 2,3,5,7\}$

Second question :

Given , the number of elements in a set C is 3

We know that , the number of subsets of a set is given by

2^n , where n is the number of elements

Thus ,

Number of subsets = (2)³ = 8

Answer 2

(a)  C =  { 2,3,5,7 }

(b) The total number of subsets is 8.

Given:

A= {x: X is a prime number less than 11}

B = {x: x is an integer such that 2 =< x <= 8}

To find:

C =A ∩ B.

The number of subsets of C has 3 elements.​

Solution:

(a) Here we can write A as

    A = { 2,3,5,7 }

    and B can be written as,

     B = { 2,3,4,5,6,7,8 }

     ∴ A∩B = { 2,3,5,7 } ∩  { 2,3,4,5,6,7,8 }

    C= A∩B = { 2,3,5,7 }

(b) It is given that the number of elements in a set C  = 3

    We know that for a set with the number of elements n,

     The total number of subsets will be $2^{n}$.

     Here, the total number of subsets = $2^{3}$

                                                               = 8

∴ The total number of subsets is 8.