Question

Out of 25 members in a office 17 like to take tea and 16 like to take coffee assume that each takes at least one of the two drinks how many like 1) both coffee and tea 2) only tea and not coffee

Answer 1

Hii Khwayish,

This is word problem on Sets in mathematics.

◆ Answer -

No of people drinking both tea & coffee = 8

No of people drinking only tea = 9

● Explanation -

Let -

A = {people drinking tea}

B = {people drinking coffee}

A∩B = {people drinking tea/coffee}

A∪B = {people drinking both tea/coffee}

# Given -

n(A) = 17

n(B) = 16

n(A∪B) = 25

# Solution -

No of people drinking both tea & coffee are -

n(A∩B) = n(A) + n(B) - n(A∪B)

n(A∩B) = 17 + 16 - 25

n(A∩B) = 8

No of people drinking only tea are -

n(A/B) = n(A) - n(A∩B)

n(A/B) = 17 - 8

n(A/B) = 9

Therefore, no of people drinking both tea & coffee are 8 and those drinking only tea are 9.

Thanks...

Answer 2

Answer:

i)8

ii)9

Step-by-step explanation:

A={people drink tea}

B={people drink coffee}

A intersect B ={people drinking tea/coffee}

A union B = {people drinking both tea & coffee}

n(A) = 17

n(B)= 16

n(A intersect B)= 25

i)   No.of people drinking both tea and coffee=

n(A intersect B) =n(A) + n(B) - n(A U B)

n(A intersect B) =17 +16 - 25

n(A intersect B) =8

ii)  No.of people drinking tea only=

n(A-B) =n(A) - n(A intersect B)

=17 - 8

=9

                                                     THANK YOU...