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.
​c) What is the probability of getting a subset of 3 elements from the power set
of C?

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\}↦A∩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