# Symbolic Logic Problem

I need to know how to construct a formal proof which shows that the sentence below is a theorem of predicate logic. The ^ sign indicates the word "or". The asterisk indicates a conditional usually indicated by an arrow. No quantifier negation rules can be used.

[(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY] * (~(EX)RX ^ (Z)(EY)SZY)

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#### Solution Preview

To solve this we consider the right hand side of the conditional, i.e.:

[(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY]

We rearrange the problem as the following argument:

[(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY]

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(Show) (~(EX)RX ^ (Z)(EY)SZY)

We can also split up and write the premises as this (using the ampersand out &o rule):

1. (X)(~RX^NX)

2. ~(EX)NX^(EY)(Z)SZY

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(Show) (~(EX)RX ^ (Z)(EY)SZY)

Of course we ...

#### Solution Summary

The validity of a symbolic logic expression is investigated. The asterisks indicating a conditional arrow is analyzed. The solution is detailed.