# Math Help - deriving sentences using inference ruels and logical dequivalences. Propositional Lgc

1. ## deriving sentences using inference ruels and logical dequivalences. Propositional Lgc

ii.) derive the statements using inference rules and logical equivalences for propositional logic.

i.(R->S)^Q
ii. (J^Q)->P
iii. Q->Z
iv.P-> -Q (v) (R->S)->(-H->J)

Code:
derive Z:

Q->Z
=Z ?

derive: -P

1. (J^Q)->P
2. P-> -Q (v) (R->S)->(-H->J)
3. ?

c.) derive -(j^Q)

1. maybe (J^Q)->P
2. P-> -Q
3.?

d.)derive -J

1.P-> -Q (v) (R->S)->(-H->J)
2.-H->J == -J->H

e.) derive H

1..P-> -Q (v) (R->S)->(-H->J)
I'm not sure how to prove it with this one.

Can you please help with this.

2. Originally Posted by Ackbeet
...I'm not sure, I'm quite new to this, perhaps you could shed some light for me. Using propositional logic, and First Order Logic.
Just the beginner discrete mathematic techniques. Unification and Resolution perhaps.

3. ii.) derive the statements using inference rules and logical equivalences for propositional logic.

i.(R->S)^Q
ii. (J^Q)->P
iii. Q->Z
iv.P-> -Q (v) (R->S)->(-H->J)
Do you need to derive each of these statements, or do you need to derive (v) from (i)--(iv)?

I'm not sure... Using propositional logic, and First Order Logic.
Not knowing what inference rules to use is like having to translate an English sentence without knowing whether the target language is French, Spanish, or Russian. You must have a textbook or course materials that list inference rules. You also should have examples of similar problems. No instructor asks you to derive a formula without going over some examples.

Unification and Resolution perhaps.
You need to know for sure. First, resolution is just one inference rule, not "rules". Second, resolution does not need logical equivalences. Third, resolution proving style is quite different from other styles, including rewriting using equivalences, because one does not prove a statement directly, but rather proves that the negation of the statement is inconsistent. Finally, you attempt doesn't look like resolution.

4. rules have been given:

1(R->S)^Q
2 (J^Q)->P
3 Q->Z
4P-> -Q (v) (R->S)->(-H->J)

the entire problem from the question has been stated in my post, that is all that was given.
Maybe the roman numerals were confusing you.

5. These are not rules but formulas, probably premises from which you need to derive some conclusion. An inference rule is a description that says how to transform formulas into other formulas. For example, the Modus Ponens rule says that from two formulas A -> B and A one can obtain the formula B.

It is quite possible that you wrote the entire question, but the description of inference rules (or other ways to prove formulas) must have been given in your textbook or course material prior to that. Without that information, it is impossible to answer your question.