There are 24 children on a school outing At lunchtime 11 of

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.

Solution

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.