FoldUnfold Table of Contents Determining the Validity of an Argument by Rules of Inference Example 1 Determining the Validity of an Argument by Rules of Inference Let $P$, $Q$, and $R$ be statements. So far we have discussed the following rules of inference: Modus Ponens: $(P \wedge (P \rightarrow Q)) \rightarrow Q$. Modus Tollens: $((P \rightarrow Q) \wedge \neg Q) … [Read more...]

## The Law of Syllogism

The Law of Syllogism Definition: Let $P$, $Q$, and $R$ be statements. Then the rule of inference known as The Law of Syllogism is given by the argument $((P \rightarrow Q) \wedge (Q \rightarrow R)) \rightarrow R$. For example, let $P$, $Q$, and $R$ be the following statements: $P$: Bob has studied for the test. $Q$: Bob will pass the test. $R$: … [Read more...]

## Valid Arguments

FoldUnfold Table of Contents Valid Arguments Valid Arguments Definition: Let $P_1$, $P_2$, …, $P_n$ be a collection of statements which we will call Premises and let $Q$ be a statement which we will call a Conclusion. Then an Argument is a formula of the form $(P_1 \wedge P_2 \wedge ... \wedge P_n) \rightarrow Q$. The argument is said to be a Valid Argument if under the … [Read more...]

## The Contrapositive, Converse, and Inverse of an Implication

FoldUnfold Table of Contents The Contrapositive, Converse, and Inverse of an Implication The Contrapositive, Converse, and Inverse of an Implication Definition: Let $P$ and $Q$ be statements and consider the implication $P \rightarrow Q$. The Contrapositive of this implication is the formula $\neg Q \rightarrow \neg P$. The Converse of this implication is the formula $Q … [Read more...]

## Logical Equivalence of Formulas

FoldUnfold Table of Contents Logical Equivalence of Formulas Logical Equivalence of Formulas Definition: Let $\varphi$ and $\psi$ be formulas that are composed of the same component statements. Then $\varphi$ and $\psi$ are said to be Logically Equivalent denoted $\varphi \Leftrightarrow \psi$ if every truth assignment to the component statements cause $\varphi$ and … [Read more...]