Question

Using the Law of Syllogism, what conclusion can you draw from the following two statements? If you miss the bus, then you will be late to school If you are late to school, then you will get detention.

Answer 1

In mathematical logic, the Law of Syllogism says that if the following two statements are true:  (1) If p , then q .  (2) If q , then r .  Then we can derive a third true statement:  (3) If p , then r .  Let p be the statement " you miss the bus", let q be the statement "you will be late to school", and let r be the statement "you will get detention".  Then (1) and (2) can be written  1) If p , then q .  2) If q , then r .  So, by the Law of Syllogism, we can deduce  3) If p , then r  or If you miss the bus then you will get detention