In a class with 42 students, 22 like blue and 27 like red. if 6 no like either colours. find : - a) how many students like both red and blue b) how many students like red only c) how many students like blue only

a) 13 students like both red and blue.

b) 14 students like only red.

c) 9 students like only blue.

Solution:

Given that total students in class = 42

Number of students do not like any color = 6

So number of students do not like any or both color = 42 – 6= 36

Let A be the set representing students who like red,

So n(A) = 22, n(B) 27  

And

a)Students who like both red and blue will be

36+n(A \cap B)=22+27

So 13 students like both red and blue.  

B)  Students who like only red:

Students who like only red=Number of students like red – Number of students like both red and blue

Students who like only red = n(B)-n(A) = 27 – 13 = 14

So 14 students like only red.

c)Students who like only blue:

Students who like only blue= Number of students like blue – Number of students like both red and blue

Students who like only blue= =22-13=9

So 9 students like only blue.              

step-by-step explanation: