2. There are 45 people at a college reunion. All of the women are smart. (hint )hint All of the men are rich. (hint )hint All of the lawyers are smart men. Everyone is a doctor or a lawyer. (hint )hint There are 12 rich women. 10 have both law and medical degrees. There are 30 rich doctors. There are 15 lawyers. There are 26 men. 1.) How many women are there?___ 2.) How many men are not lawyers?___ 3.) How many men are smart?_____ 12.) next problem

3. W S return to the problem

4. All the men are rich. M  R if and only if R  M if and only if R  W W S return to the problem R

5. Everyone is a doctor or a lawyer. D  L = U if and only if D  L D L ie: if you are not a doctor then you must be a lawyer

6. 13.) In a survey of 100 students, it was noted that: Everyone was taking English or Math All those taking Biology were also taking English and Math Everyone was taking History or Biology Everyone was taking History or Math Everyone was taking English or History 17 were enrolled in English, Math, History, and Biology 28 were enrolled in Biology 88 were enrolled in Math 76 were enrolled in English How many students were enrolled in: 1.) History?_________ 2.) History but not English?_______ 3.) Math and History?________ hint: P  Q= U if and only if P'  Q' =  if and only if P '  Q if and only if Q '  P

7. 14.) In a recent survey of students, it was noted that: Everyone was enrolled in Math or History All those taking Math were also taking Physics 8 were taking both Math and History 19 were taking Math 26 were taking Physics 20 were taking History How many students were surveyed?_______ How many were taking Physics and History?_______

8. 15.) In a recent survey of 100 people, it was noted that: All of the men watch football All of the women are happy 20 women watch football 30 men are happy 10 people do not watch football How many people are happy?______ How many people watch football?________

9. 16.) In a recent survey of people shopping at the mall, it was noted that: None of the men are happy All of the men are rich All of the happy people are teachers There are 50 men There are 90 rich people There are 85 teachers There are 20 happy rich people 10 men are teachers There are 45 rich teachers There are 30 unhappy teachers There are 95 women How many rich women are unhappy?________ How many happy people are not rich?_________