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Can It Be In Horn Form

I'm trying to understand whether R => (E <==> C) can be expressed in Horn form. How do I deal with this?
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JCW2
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JCW2
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TommySzalapskiCommented:
For Horn form I make a truth table with each of the variables and the main clause I'm testing.
For all the Fs in the main clause column all the literals must be F in the same row except for one.
So your equations truth table looks like the following. Can it go into Horn form? Look at the F rows in the last column and tell me.
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JCW2Author Commented:
By main clause, do you mean R?
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TommySzalapskiCommented:
No. The main clause is R => (E <==> C)
The easiest way to set up the truth table would probably be to put columns for
R, E, C, E<==>C, and R=>(E<==>C)
Then circle all the rows with Fs in the last column. Ignore the E<==>C column when checking for Horn form of course. Just check the literals. I add that column because I don't want to try to do it all in my head.
Generate the truth table and post it so I can help you make sure you are doing it right. I'll be on for a couple hours yet.
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JCW2Author Commented:
Using E <==> C as the main clause, I don't think I can express my problem in Horn form. Am I correct?
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JCW2Author Commented:
Disregard the last comment.
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TommySzalapskiCommented:
It is true that E<==>C cannot be expressed in Horn form. So you're probably doing it right.
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JCW2Author Commented:
From what I can see, the relevant rows are

T T F - F and
T F T - F.

Therefore, we can not express the propositional sentence in Horn form.
Is this correct?
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TommySzalapskiCommented:
100% correct.
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JCW2Author Commented:
Another thing: is it possible for a sentence to be expressed in Horn form if all literals are F in the proper row?
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TommySzalapskiCommented:
Yes. Sorry. Should have read:

For Horn form I make a truth table with each of the variables and the main clause I'm testing.
For all the Fs in the main clause column all or all but one of the literals must be F in the same row.
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JCW2Author Commented:
Thank you for your help.
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TommySzalapskiCommented:
A Horn clause has AT MOST one positive literal.
A definite clause has EXACTLY one positive literal.
So the definite clause would not work if the whole row was Ts, but Horn could.
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