Law of Syllogism (Chain Rule) - SS2 Mathematics Lesson Note

Let p be the statement “A student works very hard” and q be “A student passes his examination” and r be “a student is awarded a certificate”.

Let the statements

\(T_{1} \equiv p \rightarrow q\) is “A student works very hard implies he passes his examination”

\(T_{2} \equiv q \rightarrow r\) is “A student passes his examination implies he is awarded a certificate”

\(T_{3} \equiv p \rightarrow r\) is “A student works very hard implies he is awarded a certificate”

Then the law of syllogism is the statement \((p \rightarrow q) \land (q \rightarrow r) \rightarrow (q \rightarrow r)\) that is, if a student works very hard implies he passes his examination and if a student passes his examination implies he is awarded a certificate.

The statements \(T_{1}\) and \(T_{2}\ \)are major and minor premises respectively while \(T_{3}\) is the conclusion.