Checking Satisfiability of Compound Statement

[VinnyCee]

Homework Statement

Is this compound statement satisfiable?

$$(p\,\vee\,q\,\vee\,\neg\,r)\,\wedge\,(p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,\neg\,r\,\vee\,\neg\,s)\,\wedge\,(\neg\,p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,q\,\vee\,\neg\,s)$$

Homework 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.

The Attempt at a Solution

I "converted" the first term in the expression:

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

Now what do I do though?

 

[VinnyCee]

I figured it out!

It was simple.

The equation is satifiable.

Set p = TRUE and q = FALSE. Since it is all OR logical connectives, it was simple to find these values which make the statement true.

 

[matt grime]

I really hope you didn't just try things at random. Just use those laws above. It is quite straight forward.

 

[addison w.]

can you "VinnyCee" answer this with some explanations

*Is this compound statement is satisfiable/why?


(b) (¬p ∨ ¬q ∨ r) ∧ (¬p ∨ q ∨ ¬s) ∧ (p ∨ ¬q ∨ ¬s) ∧
(¬p ∨ ¬r∨ ¬s)∧ (p ∨ q ∨ ¬r)(¬p ∨ ¬r∨ s)