Math 110 Finite Math Exam 1 Prof. Brick
section 51 Summer ’03
Do the problems in order in your bluebook. Show your work and justify your
answers.
1. Use a Venn diagram to determine if the following is a valid syllogism:
No cartoon monster is lugubrious.
Spongebob is no cartoon monster.
Therefore, Spongebob is lugubrious.
2. Give examples of a countable infinite set and an uncountable set. Be explicit. You need
not prove your assertions, but you must identify which is which.
3. From a group of ten men and six women, you wish to form a committee of five people
with exactly two men. How many different committees can you form ?
4. A store survey of 100 students shows that 60 enjoy math classes, 50 enjoy history
classes, and only 10 don’t enjoy either. Make and label a Venn diagram with numbers that
describes the situation.
5. Use a truth table to determine the validity of the argument: “If you drive very fast then
you will get a ticket. If you get a ticket then it will cost you lots of money. Therefore, if
you drive very fast then it will cost you lots of money.”
6. How many three-card hands are possible if all of the three cards are of the same rank ?
Recall a deck of cards consists of 52 cards in 4 different suits with 13 different ranks. And
the order of the cards does not matter in a hand.
7. State the contrapositive of “If you water the lawn then it rains.”
8. Suppose Xis a set with A= (X∪B) where A={0,1,2,3}and B={2,3}. Find all
possibilities for X.
9. A computer program requires passwords that are 3 lowercase letters long. A password
is called brillig if no letter appears more than once and is called unbrillig otherwise. How
many unbrillig passwords are there ? (Hint: how many brillig passwords are there ?)