# 14.7 Direct Proofs

# 14.7 Direct Proofs

• READ pg. 701, especially the example!!!!
• (1-13) all
• this lesson is a combination of 2 previous lessons: symbolic arguments in a two-column proof format
• Remember, that in a two-column proof, each statement is written in the left-hand column. The reason for each statement is written directly across in the right-hand column.
• we can use a direct proof to show that an argument is valid.
• tomorrow we will talk about 2 other approaches to proving logical arguments: conditional proofs ans indirect proofs

the following is the answer to problem #1 of tonight's HW:

Premises:

P

P ----> Q

Q ----> R

R -----> S

Conclusion: S

Use the above Premises to arrive at the valid conclusion of S by writing a 2-column proof such as the one below:

1. P ----> Q 1. Premise

2. Q ----> R 2. Premise

3. P ----> R 3. 1, 2 LS

4. R ----> S 4. Premise

5. P ----> S 5. 3, 4 LS

6. P 6. Premise

7. therefore S 7. 5, 6 MP

For those who are still confused, below is an explanation of the above proof:

Statements 1 and 2 were given to you. But we write "premise" instead of "given" in the reason column.

Statement 3 was the valid conclusion using Statements 1 and 2. The form of valid reasoning that allows us to make that conclusion is LS. Hence, why I wrote 1", 2 LS" in the Reason column.

Statement 4 is a "premise".

Statement 5 was the valid conclusion from using statements 3 and 4. The valid form of reasoning that allows us to make the 5th statement is LS. So, in the reason column, I wrote " 3, 4 LS".

Statement 6 is a "premise".

Statement 7 was the valid conclusion from using Statements 5 and 6. The valid form of reasoning that allows us to make the 7th statement is MP. Hence, why I wrote " 5, 6 MP" in the reason column.

Pretty easy stuff. Yes, it will get more difficult. Baby steps, guys. Please feel free to post a question should you have any.

2 extra credit points to the first person to post a correct solution and explanation of the solution to problems 2-4.

3 extra credit points to the first person to post a correct solution and explanation of the solution to problems 5-7.

5 extra credit points to the first person to post a correct solution and explanation of the solution to problems 9-13. These require a legend first. Then, you must translate the argument into sympbolic form. Then, you must write a 2-column proof.

maximum of 5 points per student

can't post a solution until 3 p.m.

HAVE FUN!!!!