Discrete Mathematics Answers

Use a counterexample to disprove the following statement: "If x is greater than y, then x divided by y is greater than 1 where y ≠ 0.

Use a direct proof to show that the sum of two odd integers is even

A particular brand of shirt comes in 12 colors, has a male size version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made?

Draw the directed graph of the following relation and identify the type relation on {a,b,c,d,e}.

A) [(a,c),(b,d),(c,a),(d,b),(e,d)]

Show that the square of an even number is an even number using a direct proof.

Simplify

1. p∧(p∧q)

2. ~ (~p∨q)

3. ~ (p⇒~q)

let p(n) 1^3+2^3+....+n^3=(n(n+1)/2)2 for positive integer n