validity

Which one of the following well-formed formulae in predicate calculus is NOT valid?

Which of the following first order formulae is logically valid? Here $$\alpha \left( x \right)$$ is a first order formulae with $$x$$ as a free variable, and $$\beta $$ is a first...

Consider the following first order logic formula in which $$R$$ is a binary relation symbol. $$\forall x\forall y\left( {R\left( {x,\,y} \right) \Rightarrow R\left( {y,x} \right)}...

The following propositional statement is $$$\left( {P \to \left( {Q \vee R} \right)} \right) \to \left( {\left( {P \wedge Q} \right) \to R} \right)$$$

The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\left( {P \vee R} \right)$$, $$\left( {Q \vee \neg R} \right)...

Consider two well-formed formulas in propositional logic $$F1:P \Rightarrow \neg P$$ $$F2:\left( {P \Rightarrow \neg P} \right) \vee \left( {\neg P \Rightarrow } \right)$$ Which of...

Indicate which of the following well-formed formula are valid: