THIS IS A 2 PART HOMEWORK. PLEASE DO SEPARATE FILES FOR EACH PART.

PART 1

**Q1**

Which of the following are **statements**?

Ten is less than seven.

How old are you?

She is very talented.

There are life forms on other planets in the universe.

**Q2**

What is the truth value of the following statements:

If 8 is odd,then 6 is odd.

If 8 is even, then 6 is odd.

**Q3**

Let A = "The villain is French."

B = "The hero is American."

C = "The heroine is British."

D = "The movie is good."

Translate the following statements into symbolic notation:

A British heroine is a necessary condition for the movie to be good.

The hero is not American, but the villain is French.

PART 2 PART 2 PART 2 - PLEASE START A NEW PAGE.

Q1

Which of the following are statements? 4 points (1 point each)

1. She is mathematics major.

2. 128=2^6

3. All that glitters is not gold.

4. Sleep tight and don’t let the bedbugs bite.

Q2

Let A, B, and C be the following statements:

A: John is healthy

B: John is wealthy

C: John is wise

Use A, B, and C as defined above to translate the following statements into symbolic

form.4 points (1 point each)

1. John is healthy and wealthy but not wise.

2. John is not wealthy but he is healthy and wise.

3. John is neither healthy, wealthy, nor wise.

4. John is wealthy, but he is not both healthy and wise.

Q3

Justify each step in the proof sequence below for [A → (B∨C)] ∧ B’ ∧ C’ → A’

(1 point)

1. A → (B∨C)

2. B’

3. C’

4. B’∧C’

5. (B∨C)’

6. A’

Q4

Use propositional logic to prove that the argument is valid (hint: the last A’ has to be

inferred). Justify each step. (1 point)

(A → C)∧(C → B’)∧B → A’

Subject | Mathematics |

Due By (Pacific Time) | 11/21/2014 12:00 pm |

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