Discrete Mathematics Answers

State whether the following graph g1 and g2 are isotropic or not

Create a schematic diagram of all odd numbers from 20 to 45

Use quantifiers and predicates with more than one vari-

able to express these statements.

a) There is a student in this class who can speak Hindi.

b) Every student in this class plays some sport.

c) Some student in this class has visited Alaska but has

not visited Hawaii.

d) All students in this class have learned at least one pro-

gramming language.

) There is a student in this class who has taken ev-

ery course offered by one of the departments in this

school.

1) Some student in this class grew up in the same town

as exactly one other student in this class.

Choosing the correct answer step by step

A discrete mathematics class contains I mathematics

major who is a freshman, 12 mathematics majors who

are sophomores, 15 computer science majors who are

sophomores. 2 mathematics majors who are juniors. 2

computer science majors who are juniors, and I computer

science major who is a senior. Express each of these state-

ments in terms of quantifiers and then determine its truth

value.

a) There is a student in the class who is a junior.

b) Every student in the class is a computer science ma-

jor.

c) There is a student in the class who is neither a math-

ematics major nor a junior.

d) Every student in the class is either a sophomore or a

computer science major.

e) There is a major such that there is a student in the

class in every year of study with that major.

Choosing the correct answer step by step

For each relation below, determine if they are reflexive, symmetric, anti-symmetric, and transitive.

(a) X= { 1, 2, 3, 4}

R1={(1, 2),(2, 3),(3, 4)}

(b) X = {a, b, c, d, e}

R1 = { (a, a), (a, b), (a, e), (b, b), (b, e), (c, c), (c, d), (d, d), (e, e) }

(c) X= { 1, 2, 3, 4}

R1= {(1, 3),(1, 4),(2, 3),(2, 4),(3, 1),(3, 4)}

1.Draw the digraph of the following relations.

(a) R = {(1, 2), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4}

(b) R={(1, 2), (2, 1), (3, 3), (1, 1), (2, 2)} on X = {1, 2, 3}

Find all substrings of the string babc.

1. Given ϕ2 = 5. Is ϕ increasing, decreasing, non-increasing and/or non-decreasing?

1.b is defined by bn = n(−1)n, n ≥ 1

(a) Find Σ when 4 is on top, i=1 at the bottom and b_i at the right hand side

(b) Is b increasing, decreasing, non-increasing or non-decreasing?

4. v defined by vn = n! + 2, n ≥ 1.

(a) Find v3

(b) Find  Σ 4 on top , i=1 at the bottom and V_i on the right hand side of Sigma

(c) Is v increasing, decreasing, non-increasing or non-decreasing?