Part II follow these steps:

1. Highlight the main operators for the premises and conclusion. Each premise and conclusion have only one main operator. (See #2 below)
2. Put True (T) under all of the premise main operators. (See #2 below)
3. Put False (F) under the conclusion main operator. (See #2 below)
4. Unless otherwise directed, determine the truth values for the conclusion's atomic statements (capital letters).
5. Remember, if you assign a truth value to one atomic statement (capital letter), then all of the same letters in that row get the same truth value. For example, if in row one, "Q" is assigned True, then all of the "Q's" in row one are assigned "True."
6. A contradiction occurs if an operator or atomic statement would have to be both True and False to make the argument invalid.
7. If you can fill in the truth values for a single row without having any contradictions, then the argument is invalid because it is possible for the argument to have true premises and a false conclusion. Mark the argument as invalid.
8. If all the rows of the argument contain contradictions, then the argument is valid because there is no truth value combination that will make the premises true and the conclusion false. Mark the argument as valid. In addition, highlight the area of the argument where the contradiction occurs.

Exercise 5.5, Part II. Use indirect tables to determine whether the following arguments are valid or invalid. If the argument is valid, be sure to highlight the exact location of the contradiction. Make sure to indicate if the argument is valid or invalid. (6 points)

3. P (Q R)

R S

P S

P

(Q

R)

/

R

S

//

P

S

5. W (X Y)

X (Y Z)

W (X Z)

W

(X

Y)

/

X

(Y

Z)

//

W

(X

Z)

6. A (B v C)

C (D E)

A ~E

A

(B

C)

/

C

(D

E)

//

A

~

E