The notation \(a | b\) represents a relationship between the integers \(a\) and \(b\) and is simply a shorthand for “\(a\) divides \(b\).” "Divides" as in \(a | b\) is a relation (true or false), whil...The notation \(a | b\) represents a relationship between the integers \(a\) and \(b\) and is simply a shorthand for “\(a\) divides \(b\).” "Divides" as in \(a | b\) is a relation (true or false), while "divided by" as in \(\dfrac{a}{b}\) or \(a/b\) is an operation (results in a number) .
The first one is the fallacy of the inverse or the denial of the antecedent: \[\begin{array}{cl} & p \Rightarrow q \\ & \overline{p} \\ \hline \therefore & \overline{q} \end{array}\] This in effect pr...The first one is the fallacy of the inverse or the denial of the antecedent: \[\begin{array}{cl} & p \Rightarrow q \\ & \overline{p} \\ \hline \therefore & \overline{q} \end{array}\] This in effect proves the inverse \(\overline{p}\Rightarrow \overline{q}\), which we know is not logically equivalent to the original implication.
