Discrete Math- Math 203

1. Determine whether the number 77 is even or odd, and verify your statement by applying the definition.

2. Determine whether the number 77 is prime or composite, and verify your statement by applying the definition.

3. Verify that the number 22.819 is a rational number by applying the definition.

4. Convert the rational number, 12.45454545.... into a fraction of integers.

5. Consider the numbers, d = 6 and n = 24. Determine whether or not d|n and verify your choice by applying the definition.

6. Give the negation of the mathematical statement:

There exists a real number, x, such that x^2 < Pi.

7. Apply the statement of the quotient-remainder theorem to the numbers d = 6 and n = 22.

8. Provide the three main properties of the "=" sign and provide examples.

9. Apply the statement of the prime factorization theorem to the number: 84.

If I want to take a group of n-many people and line up all n of them, then show me why you can use either the permutation or combination formulae if we assume that 0! = 1.