Logic and Proof

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Argument
An argument is a sequence of statements.
All statements but the first one are called
assumptions
or
hypothesis
.
The final statement is called the
conclusion
.
An argument is
valid
if:
whenever all the assumptions are true, then the conclusion is true.
If today is Wednesday, then yesterday is Tuesday.
Today is Wednesday.
Yesterday is Tuesday.

Modus Ponens
If p then q.
p
q
p
q
p
→
q
p
q
Modus ponens is Latin meaning “method of affirming”.

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Modus Tollens
If p then q.
~q
~p
p
q
p
→
q
~q
~p
Modus tollens
is Latin meaning “method of denying”.