This topic is from sets in the COT 3103 Discrete Computational Analysis class th

Question

This topic is from sets in the COT 3103 Discrete Computational Analysis class

this to be an inclusion-exclusion principle question where there was some intersection, or in this case some grilled cheese sandwiches that had both American and Cheddar cheese.

Suppose you are planning a party for ten friends. You decide to make grilled cheese sandwiches to serve at the party, no more than one sandwich per person. Seven of your friends say they want American cheese. Four say they want cheddar. Two are vegans and have a salad instead of a sandwich.

a) How many grilled cheese sandwiches do you make?

b) How many sandwiches have only American cheese?

c) How many sandwiches have both American cheese and cheddar?

Explanation / Answer

two are vegans and had salas instead of snadwich

thus total 8 sandwich required

out of that 7 says they want American cheese and four says they want cheddar

ie. n(A)=7 n(C)= 4 and total n(A u C ) =10

we know that

n(A u C) = n(A)+n(C) - n(A ^ C)

8=7+4-n(A ^ C)

n(A ^ C) = 11-8=3

i.e three demand for both American and cheddar cheese

a)

total 8 grilled chill sandwich made

b)

only American cheese sandwich = n(A) - n(A ^C) = 7- 3=4

c)

n(A ^C )=3 snadwich has both American and chedder cheese

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