Math 170 Project #11

1. Math 170 Project #11 Part 1 Jeffrey Martinez Bianca Orozco Omar Monroy

2. Chapter 2 Section 3 Problem 30 Identify the rules of inference that guarantees its validity. If this computer program is correct, then it produces the correct output when run with the test data my teacher gave me This computer program produces the correct output when run with the test date my teacher gave me This computer program is correct.

3. Statements Assume P and Q represent two sentences that are either true or false, but not both. Let P = This computer program is correct Let Q = This computer program produces the correct output when run with the test data my teacher gave me. When two statements are combined with an if and then they become a conditional statement.

4. Conditional Statements Notation: If P, then Qor P implies Qor PQ The new statement “PQ” is true in all cases except when: Statement P is true and Statement Q is false.

5. Argument Replace the statements with P and Q PQ Q P When statements are put in such a sequence it is known as an argument. signals the conclusion of the argument

6. Rule of Inferences The argument given appears the most similar to the following rules of inferences: • Modus Ponens PQ P Q 2. Modus Tollens PQ ~Q ~P

7. Solution As you can see neither of these rule of inferences exactly matches the argument we were given. Considering 1. Modus Ponens, the reason our given argument is false is because of the Converse Error. Considering 2. Modus Tollens, the reason our given argument is false is because of the Inverse Error. Our argument is invalid because of either the converse error or the inverse error, but not both.

8. Bibliography Epp, S. S. (2010). The Logic of Compound Statements. In Discrete Mathematics with Applications (pp. 24, 39, 40, 51, 53, 54, 58, 62…). Belmont, CA: Brooks/Cole-Thomas Learning.