Discrete Mathematics Answers

In a survey on the gelato preferences of college students, the following data was

obtained: • 78 like mixed berry • 32 like irish cream • 57 like tiramisu • 13 like

both mixed berry and irish cream • 21 like both irish cream and tiramisu • 16

like both tiramisu and mixed berry • 5 like all three flavours above • 14 like none

of these three flavours How many students were surveyed?

There are 38 different time periods during which classes at a university can be

scheduled. If there are 677 different classes, how many different rooms will be

needed?

Show that in any set of six classes, each meeting regularly once a week on a

particular day of the week, there must be two that meet on the same day,

assuming that no classes are held on weekends.

Suppose 5 points are chosen at random in the interior of an equilateral triangle

T where each side has length two inches. Show that the distance between two of

the points must be less than one inch.

Consider a tournament with n players where each player plays against every

other player. Suppose each player wins at least once. Show that at least 2 of the

players have the same number of wins.

Find the minimum number n of integers to be selected from S = {1, 2, . . . , 9} so 

that: (a) The sum of two of the n integers is even. (b) The difference of two of the 

n integers is 5.

If A = {1, 2, 3, 4, 6, 12} then define a relation R by aRb if and only if a divides b. Prove that R is a partial order on A.

Suppose that A = {2, 4, 6}, B ={2, 6}, C ={4, 6}, and D ={4, 6, 8}. Determine which of these sets

are subsets of which other of these sets.

A pet store keeps track of the purchases of customers over a fours hour period. The store manager classifies purchases as containing a dog product, a cat product, a fish product, or product for a different kind of pet. He found!

83 purchased a dog product

101 purchased a cat product

22 purchased a fish product

31 purchased a dog and a cat product

8 purchased a dog and a fish product

10 purchased a cat and a fish product

6 purchased a dog, a cat, and a fish product

34 purchased a product for a pet other than a dog, cat, or fish.

Draw a Venn diagram to find that:

(1) How many purchases were for a dog product only?

(ii) How many purchases were for a cat product only?

How many purchases were for a dog or a fish product?

(iv) How many purchases were there in total?

Determine how many bit strings of length 5 can be formed, where the first bit is 0 and three consecutive 0s are not allowed.