# There are 24 children on a school outing. At lunch-time 11 of them ate sandwich, 9 ate banana, n of them ate neither a sandwich nor banana. By using venn. diagram, find A) the smallest possible...

There are 24 children on a school outing. At lunch-time 11 of them ate sandwich, 9 ate banana, n of them ate neither a sandwich nor banana.

By using venn. diagram, find A) the smallest possible value of n, B) the largest possible value of n.

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### 2 Answers

Number of children who ate banana = N(B) = 9

Number of children who ate sandwich = N(S) = 11.

Therefore number of chidren who did not eat any thing = 24 - N(A u B).

If N(AuB) = 11+9 if N (A&B) = 0. Then N(AUB)' = number of children neither ate banana or sanwhich = 24-(11+9) = 4 is the lest.

N(AuB) = 11 when all the sandwich eaten childen also ate banana. In this case, N(AUB)' = number of children who did neither eatsandwich nor eat eat banana = 1- N(AUB) = 24 -11 = 13 is the maximum possible number.

Out of the 24 students on the school outing :

11 ate sandwich, so 24 - 11 = 13 did not eat a sandwich.

9 ate a banana, so 24 - 9 = 15 did not eat eat a banana.

Now the n of them ate neither a sandwich nor a banana.

If the set of those ate a banana lies within those who ate sandwich, those who ate neither is 24 - 11 = 13.

If there are no common elements in the set who ate sandwich and those who ate banana the number who ate neither is 24 - 11- 9 = 4.

**Therefore the smallest possible value of n is 4 and the largest value of n is 13. **