Discrete Mathematics Answers

In a survey of 120 professors, a research found that 50 preferred traditional method of teaching, 78

preferred computer-aided method, and 66 preferred group method. In addition, 36 preferred any of

the two methods of teaching and 24 professors preferred them all.

a. Find the number of professors who prefer at least one of the teaching methodologies

b. Find the number of professors who do not prefer any of the teaching methodology

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6, 7}, C = {2, 3, 8, 9}. Perform the following

a.

𝐴∪𝐵

b.

𝐴∩𝐵

c.

𝐴∪𝐶

d.

𝐴∩𝐶

Use a Venn Diagram to illustrate the following:

a. The subset of odd integers in the set of all positive integers not exceeding 10

b. The set of all months of the year whose names do not contain the letter R in the set of all months

of the year

Let R be a relation on the set A={1,2,3,4,5,6} defined by R= {(a,b):a+b is less than or equal to 9}. What are the elements of R?

How many strings of eight uppercase English letters are there

a) that start with X, if no letter can be repeated?

during a high school spirit week student dress up in costumes. a cash price is given to students with the best costume the organization committee has $1000 to give away over 5 days the committee wants to increase the price by $50 each day how much should the committee give away on the first day?

There are 10 girls and 7 boys in a class and need to select 4 students as a school representative. In how many ways can we select of 2 girls and 2 boys?

How many strings can be formed in the length of 5 strings from the word DISCRETE?

Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.

a. Show that f is one-to-one and onto.

b. Show that g is one-to-one and onto.

c. Determine the composition function g o f

d. Determine the inverse functions f ^-1 and g ^-1 .

e. Determine the inverse function (g o f) ^-1 of g o f and the composite f ^-1 o g ^-1