Deductive Reasoning

Syllogism:
three parts, a=b, b=c, thus a=c
For an example:
All basketballs are orange.
Carrots are orange.
All basketballs are carrots.

Modus Ponens:
if p then q,
p,
therefore q.
For an example:
If it is raining, then I will use my umbrella.
It is raining,
Therefore, I will use my umbrella.

Modus Tollens:
if p, then not q
not q,
therefore not p.
If Danny smokes, he will get lung cancer.
Danny does not have lung cancer,
Therefore, Danny does not smoke.

In class, we were presented with several examples that were not true but were still valid. I know my examples above are not true but they are valid, right?