Determining the Truth Value of Complex Statements

In order to determine the truth value of a complex statement, you first need to determine the truth value of its components. If the statement is very complex, this can be tricky. This assignment will give you a chance to practice this skill.

Directions:

1. Number the operators in the order that you will determine their truth values. (Note: Two or more operators can have the same number if there is no reason the truth value of one should be determined before the truth value of another.)

2. Assume that A, B, and C are true and X, Y, and Z are false. Determine the truth value of the components and the entire statement, circling the truth value under the main operator, i.e., the last operator you determine.

Determine the truth value of components in the following order:

1. Simple statements.

2. Negations of simple statements.

3. Any of the other operators found in parentheses.

4. Negations of complex statements in parentheses (the negation is found just outside parentheses).

5. Any of the other operators found in brackets.

6. Negations of complex statements in brackets.

7. Any of the other operators not contained in parentheses and brackets.

Example: ~ (A → B) & [(~ X v Y) & C]

3 2 5 1 2 4

F T T T (F) T F T F T T

1. Z v (A → ~ Y)

2. ~ (C v X) & ~ B

3. (~ X → ~ B) v (A & C)

4. (Y & ~ A) → (~ B → C)

5. (B v ~ Y) & ~ (C v X)

6. ~ [A v (~ B & ~ C)]

7. X → [~ (C v B) & Z]

8. [Y & ~ (X v Y)] v ~ A

9. (B & ~ C) v [~ X v (Z → A)]

10. ~ [(C & Y) v (~ X & Z)] v (Y → ~ A)