Week 1 Mth221

Math Assignment 1

Jason E. Martin

Math 221

September 21, 2013

Al Hamdo

Math Assignment 1

2. A machine has nine different dials, each with five settings

labeled 0, 1, 2, 3, and 4.

a) In how many ways can all the dials on the machine be

set?

Answer: 1,953,125

b) If the nine dials are arranged in a line at the top of the

machine, how many of the machine settings have no two

adjacent dials with the same setting?

Answer: 327,680

8. In how many ways can the letters in WONDERING be

arranged with exactly two consecutive vowels?

Answer: 42

Chapter 2 Questions

2.1 2.

Identify the primitive statements in Exercise 1.

Answer:

In 2003 George W. Bush was the president of the United States. (Primitive Statement)

Fifteen is an even number. (Primitive Statement)

If Jennifer is late for the party, then her cousin Zachary will be quite angry. (Primitive Statement)

As of June 30, 2003, Christine Marie Evert had won the French Open a record seventimes. (Primitive Statement)

2.2 4.

For primitive statements p, q, r, and s, simplify the compound

statement

[[[(p ∧ q) ∧ r] ∨ [(p ∧ q)∧¬r]] ∨ ¬q]→s.

Answer:

let (p^q)=t

=[[[t^r]v[t^~r]]v~q]->s

=[[t^(rv~r)]v~q]->s By distributive law

=[[t^To]v~q]->s By inverse law

=[t v ~q]->s By identity law

=[p^qv~q]->s Replacing t by (p^q)

=[p^To]->s By inverse law

=p->s By identity law

=~pvs Logically equivalence

2.3 4.

For each of the following pairs of statements, use Modus

Ponens or Modus Tollens to fill in the blank line so that a valid

arguement is presented.

a) If Janice has trouble starting her car, then her daughter

Angela will check Janice’s spark plugs.

Janice had trouble starting her car.

∴________________________________________________________

Answer:...