Expert: Cynthia Watanabe - 10/19/2006

Question
what is the difference and can you give me some examples?

Answer
Gina,

Let's look at Law of detachment first.

If p and (p implies q), then we conclude q.
Remember both parts of the hypothesis MUST BE TRUE.

So, let's look at a couple of statements.

p: This toy is a truck.
q: This toy has 4 wheels.

Rememeber p implies q means "If p, then q."
So let's substitute. If this toy is a truck, then it has 4 wheels.

Suppose "The toy is a truck." is true. And suppose "if this toy is a truck, then it has 4 wheels" is also true.

What can you conclude?  Well, you can conclude that the toy has 4 wheels.  That's the Law of Detachment. It's "sort of like" substitution.
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Now, let's look at Law of Syllogism.

Here you have 3 statements: p, q, & r. Notice that in the Law of Detachment you only had 2 statements to work with.

Example: p: Mary is shorter than Debbie.
q: Debbie is shorter than Joan.
r: Joan is shorter than Maria.

If (p implies q) and (q implies r), then we conclude (p implies r).

Let's substitute:

p implies q: If Mary is shorter than Debbie, then Debbie is shorter than Joan.

q implies r: If Debbie is shorter than Joan, then Joan is shorter than Maria.

We conclude that p implies r. So by Law of Syllogism,

If Mary is shorter than Debbie, then Joan is shorter than Maria.

This is like the Transitive Property.

A key difference to remember is that Detachment works with only 2 statements while Syllogism works with 3 statements.

Here are some answers for the difference between the 2 laws from other websites:
Here's one from another expert:http://experts.about.com/q/Geometry-2060/law-detachment-syllogism.htm
or
http://answers.yahoo.com/question/index?qid=20060927165117AA1LfAE

Keep asking questions! Take care, Cynthia