syllogisms, modus ponens, modus tollens

Syllogisms, Modus Ponens, and Modus Tollens are different than each other. syllogisms have have three statments that contain two terms in each statement. the middle term is repeated. (A=B, B=C, A=C) with a syllogism, the statement goes from being general to being specific. it contains a major premise, a minor premise, and a conclusion. even though modus ponens and modus tollens are similar, they are also different. the main difference between a modus ponen and a modus tollen is that ponen is positive and tollen is negative. for modus ponens, the formula is...
if p, then q
p
-----------------
therefore, q

but for modus tollens, the formula is...
if p, then q
not q
----------------
therefore, not p
an example of this would be...
if i live in california, then i live in the united states.
if i dont live in the united states, then i dont live in california.