Question

in a group of 40 students 26 students like orange but not banana while 32 students like orange . if all the students like atleast one of the two fruits . find the number of students who like (1) both orange and banana (ii) only banana.

Answer 1

i) No of students like oranges =32

No of student like oranges but dislike bananas =26

No of students like both oranges and banana are 32-26=6

Answer=6

Answer 2

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Here's your answer...

Let the set of people liking oranges be O and bananas be B.

Then n(O) = 32 and n(O-B) = 26

The set O contains people liking both bananas and oranges in it, while the set O-B does not.
So n(O) - n(O-B) = n(OnB)
n(OnB) = 32-26 = 6

The total people in the class will be the sum of the people who like bananas but not oranges, the people who like oranges bit not bananas, and the people who like both oranges and bananas.

n(AuB) = n(O-B) + n(B-O) + n(OnB)
40 = 26 + n(B-O) + 6
n(B-O) = 8

6 people like both the fruits while 8 people like only bananas.

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