Hypothetical syllogism
Much like modus ponens and modus tollens, hypothetical syllogism (sometimes abbreviated as HS) contains two premises and a conclusion. It is, however, slightly more complicated than the first two. In short, it states that if one thing happens, another will as well. If that second thing happens, a third will follow it. Therefore, if the first thing happens, it is inevitable that the third will too.[3] It is shown below in logical form.
If A, then B
If B, then C
Therefore if A, then C
When put into words it looks like below.
If it rains today, I will wear my rain jacket
If I wear my rain jacket, I will keep dry
Therefore if it rains today, I will keep dry
Disjunctive syllogism
Disjunctive syllogism (sometimes abbreviated DS) has one of the same characteristics as modus tollens in that it contains a premise, then in a second premise it denies a statement, leading to the conclusion. In Disjunctive Syllogism, the first premise establishes two options. The second takes one away, so the conclusion states that the remaining one must be true.[3] It is shown below in logical form.
Either A or B
Not A
Therefore B
When A and B are replaced with real life examples it looks like below.
Either you will see Joe in class today or he will oversleep
You did not see Joe in class today
Therefore Joe overslept
Disjunctive syllogism takes two options and narrows it down to one.