2.4 DEDUCTIVE
REASONING
Playing the game of logic well
Law of Detachment
[(p>>q)^p]>>q
If p, then q is True
And p is True
Then q is True
An example: If a vehicle is a car, then it has four wheels.
A Cadillac is a car.
Then (by the law of detachment) it (the caddy) has four
wheels.
Law of Syllogism
[(p>>q)^(q>>r)] >>(p>>r)
If p, then q is True
And If q, then r is True
Then If p, then r is True
An example: If Gertrude takes the Cadillac for a spin, she will
stop at the post office.
If she stops at the post office, then she will buy stamps.
Thus (by the law of syllogism) If Gertrude takes the Cadillac for
a spin, then she will buy stamps.
Cornerstone of Geometry
These are two of the laws of logic that provide a system for
reaching logical and always true conclusions.
This system is called Deductive Reasoning