In a scientific study of 233 imaginary people, each eats at least one meal every day. Of these, 91 eat breakfast, 152 eat lunch and 177 eat dinner. Also, 190 eat either breakfast or 1 lunch, 205 eat either breakfast or dinner, and 226 eat either lunch or dinner. a) How many people eat both breakfast and lunch? b) How many people eat all three meals? c) How many people eat both breakfast and lunch, but not dinner?
I know that I have to use inclusion and exclusion principles of cardinality, but I am really confused as to how to do this?
Start by letting $B$ = people who eat breakfast, $L$ for lunch, and $D$ for dinner.
Express the information you're given in the set notation, e.g. $N(B)=91$, so you can substitute into the formulas. Then part (a) would be asking for $N(B \cap L)$; (b) and (c) are similar in spirit. Does that help?