Discrete Math

Find the prime factorization of 24.

Find the prime factorization of 75.

Find the prime factorization of 84.

What is the prime factorization of 50?

Write the prime factorization of 120.

Write the prime factorization of 280.

Write the prime factorization of 540 using the factor tree method.

Find the prime factorization of 10,800.

Prove that no integer is both even and odd using proof by contradiction.

Show that $\sqrt{2}$ is irrational.

Prove that $(A - B) \cap (B - A) = \emptyset$.

Prove that if $n^2$ is even, then $n$ is even using a proof by contrapositive.

If $3|a^2$ then $3|a$ for any integer $a$.

Prove that in every tree, the number of edges is equal to the number of vertices minus one.

Given graphs T_1 and T_2, where the number of edges in T_1 is 17, and the number of vertices in T_2 is 2 times the number of vertices in T_1, find V_1 and E_2.

(Note: E_1 = 17, V_1 = E_1 + 1, V_2 = 2 \times V_1, E_2 = V_2 - 1)

Is it possible to have a graph where the number of vertices is equal to the number of edges plus one, but the graph is not a tree?

A graph T is a tree if and only if between every pair of distinct vertices of T there's a unique path.

A graph F is a forest if and only if between any pair of vertices in F there is at most one path.

Any tree with at least two vertices has at least two vertices of degree one.

Let T be a tree with V vertices and E edges. Then, E (the number of edges) is equal to V (the number of vertices) minus one.