(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is this compound statement satisfiable?

[tex](p\,\vee\,q\,\vee\,\neg\,r)\,\wedge\,(p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,\neg\,r\,\vee\,\neg\,s)\,\wedge\,(\neg\,p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,q\,\vee\,\neg\,s)[/tex]

2. Relevant equations

I guess you are supposed to use the following instead of truth tables somehow:

Logical equivalences - Domination, Idempotent, Double negation, Commutative, De Morgan's, Absorption, Negation, Associate, Distributive.

3. The attempt at a solution

I "converted" the first term in the expression:

[tex](p\,\vee\,q\,\vee\,\neg\,r)\,\equiv\,\left[(\neg\,p\,\longrightarrow\,q)\,\vee\,\neg\,r\right][/tex]

Now what do I do though?

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# DISCRETE MATH: Which of these compound propositions is satisfiable? No use truthtable

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