Discrete Mathematics Answers

Give an example of a function which represents all types of a function. Find the composite

function (f o g) (x) given that

f = {(1,6), (4,7), (5,0)} and g = {(6,1), (7,4), (0,5)}

There are 70 women in class. Each play at least one game of the following games; volleyball, basketball, table tennis.

20 play volleyball only,10 play basketball only and 6 play table tennis.

4 play all the games and an equal number play 2 games only.

A) Illustration these informations on a Vern diagram.

i) Find the number of women who play volleyball.

There were 100 students in the library who responded to how they completed their research paper. • 18 students only used the periodicals. • 29 students used the web and books. • 15 students used books, the web, and periodicals. • 40 students used books and periodicals. • 20 used the web and periodicals. • 60 students used books. • 7 students did not use the web, nor books, nor the periodicals. a) Represent this information with a Venn diagram. (8 marks) b) How many students only used the web in their research? (2 marks) c) How many students used books or periodicals?

draw a binary search tree by inserting the values 50, 76, 21, 4, 32, 64, 15, 52, 14, 100, 83, 2, 3 and 70.

A class contains 10 students with 6 boys and 4 girls. Find the number of ways: i. A 4 member committee can be selected from the students. ii. A 4 member committee with 2 boys and 2 girls can be selected from the students. iii. A 4 member committee at least 3 boys can be selected from the students.

Q3:

List the 16 different relations on the set {0,1}.

Note: No partial credit would be admissible in this question.

Q2:

Let R be the parent relation on the set of all people (see Example 21 in section 9.1

of the book). When is an ordered pair in the relation R^3?

SUGGESTED TEXT:

·     Keneth H. Rosen. Discrete Mathematics and its Applications. 7th edition.

Q1:

Determine whether the relation R on the set of all people is reflexive, symmetric,

antisymmetric, and/or transitive, where (a,b) ∈ R if and only if

a) a is taller than b.

b) a and b were born on the same day.

c) a has the same first name as b.

d) a and b have a common grandparent.

given that the function f(x) = 4x + 1 , find a formula for f^-1(x)

Define a binary relation P from R to R as follows: for all real numbers x and y, (x,y)∈P⇔x=y^2. Is P a function? Explain.