Spring ’00 Math 110 Exam 1 Prof. Brick
MA110-5
Do the problems in order in your bluebook. Show your work.
1. Use a Venn diagram to determine whether or not the following is a valid syllogism:
No doctor is poor.
Lew Zer is no doctor.
Therefore, Lew Zer is poor.
2. State the contrapositive of “If you exercise regularly then you are in good shape.”
3. Use a truth table to determine whether or not the wffs p→qand (¬p)∨qare equivalent.
4. Draw a Venn diagram for three nonempty sets A,B, and C(in a universal set U) where
each two intersect but all three don’t. In it shade the region A∩Bc∩Cc.
5. In a dorm holding 959 students, 463 are taking Math, 289 are taking Physics, and 222
are taking Chemistry. Suppose 25 of these are taking all three, 83 are taking Math and
Chemistry, 47 are only taking Chemistry, and 66 are taking Math and Physics. What
percentage of students in the dorm are taking at exactly one of these three classes ? Draw
and label a Venn diagram. Explain each step of your reasoning.
6. How many (5 card) poker hands are flushes (i.e., five cards of the same suit) ? Explain
where each part of your answer comes from.
7. From a group of twelve men and six women, you wish to form a committee of four men
and three women. How many different committees can you form ? Explain where each
part of your answer comes from.
8. Suppose A={1,2}and B={−1,1}. Find all subsets of A∪B.
