# Math Help - Derivation rules

1. ## Derivation rules

Hello,

I have recently started this course and I believe it is the beginner course. At my school it is labeled CSC 221.

I am currently working on a homework assignment and I am having a little bit of trouble.

The problem states:
Assuming all of the following are correct.

Processor B is not working and processor C is working.
Processor A is working if and only if processor B is working.
At least one of the two professors A, B is not working.

Let a = “A is working”, b = “B is working” and c = “C is working”.

a. Write each status report in terms of a, b, and c, using the symbols of formal logic.

¬b ^ c
a→ b
¬a ¬b

b. How would you justify the conclusion that B is not working? (In other words, given
the statements in part (a), which derivation rule allows you to conclude ¬b)

part b I am having difficultly finding what exact rule it is looking for. I don't understand all the rule completely which is making it a little difficult specially with all these new concepts being thrown at me at one time. Some are self explanatory others I am unsure.

If b is not working then c is working but a is not. therefore the only working processor would be c. That is what I get if be is not working. But I don't know how to write that down. or what rule I use to logically prove that.

Thanks

2. Originally Posted by Newskin01
Hello,

I have recently started this course and I believe it is the beginner course. At my school it is labeled CSC 221.

I am currently working on a homework assignment and I am having a little bit of trouble.

The problem states:
Assuming all of the following are correct.

Processor B is not working and processor C is working.
Processor A is working if and only if processor B is working.
At least one of the two professors A, B is not working.

Let a = “A is working”, b = “B is working” and c = “C is working”.

a. Write each status report in terms of a, b, and c, using the symbols of formal logic.

¬b ^ c
a→ b
¬a ¬b

b. How would you justify the conclusion that B is not working? (In other words, given
the statements in part (a), which derivation rule allows you to conclude ¬b)

part b I am having difficultly finding what exact rule it is looking for. I don't understand all the rule completely which is making it a little difficult specially with all these new concepts being thrown at me at one time. Some are self explanatory others I am unsure.

If b is not working then c is working but a is not. therefore the only working processor would be c. That is what I get if be is not working. But I don't know how to write that down. or what rule I use to logically prove that.

Thanks

Part (a) is incorrect: line 2 must be $a\leftrightarrow b$

As for part (b): from line 1 in part (a) it follows at once that $\neg b$

Tonio