Discrete Mathematics Answers

Describe two situations that can be modelled with a Graph. Describe the graph model that you will use.
Describe two situations that can be modelled with a Tree. Describe the tree model that you will use.

Describe two situations that can be modelled with a tree . Describe the graph model that you will use

Describe two situations that can be modelled with a Tree. Describe the graph model that you will use.

Describe two situations that can be modelled with a Graph. Describe the graph model that you will use

Prove that for all integers n with 1≤n≤10,n^2 −n+11 is prime.

Prove that for all positive integers n
3^n +7^n −2 is divisible by 8

Let X = {0, 1, 2}. Consider the power set P(X). Recall that P(X) = {A such that A ⊆ X}.
Determine if each statement is true or false. (a) X ∈ P(X).
(b) ∅∈P(X)
(c) X ⊆ P(X).
(d) {0,2}∈P(X) (e) {0,2,1} ∈ X (f) {0}⊆X
(g) {{0}} ⊆ P(X)

Define the relation R as
R = {(a, b)|a, b ∈ Z, 4 divides a − b}. Show that R is reflexive, transitive and symmetric.

Prove that 3n2 − n + 10 is an even integer for all integers n. (Hint: Prove the statement
true when n is odd, then prove it is true when n is even.)

Write down the contrapositive of the statement “If 3n2 + 4 is even then n is even.” Then prove the statement for all integers n.