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(Solved): Use inference rules to show that the following argument is valid. 1) Use the i ...
???????Use inference rules to show that the following argument is valid.
1) Use the inference rules to show that the following argument is valid. \[ \begin{array}{l} \forall \mathrm{x}(\mathrm{P}(\mathrm{x}) \vee \mathrm{Q}(\mathrm{x})) \\ \forall \mathrm{x}(\neg \mathrm{Q}(\mathrm{x}) \vee \mathrm{S}(\mathrm{x})) \\ \forall \mathrm{x}(\mathrm{R}(\mathrm{x}) \rightarrow \neg \mathrm{S}(\mathrm{x})) \\ \exists \mathrm{x} \neg \mathrm{P}(\mathrm{x}) \\ \therefore \quad \exists \mathrm{x} \neg \mathrm{R}(\mathrm{x}) \end{array} \]
Expert Answer
if we can reach the conclusion using valid rules of inference then we say the given argument is valid. 1.?x(P(x)?Q(x)) 2.?x(¬Q(x)?S(x)) 3.?x(R(x)?¬S(x