Download An Introduction to Logic

Why Logic?
A proof of any form requires logical
reasoning.
Logical reasoning ensures that the
conclusions you reach are TRUE - as
long as the rest of the statements in
the argument are also TRUE.
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For example:
All Mustangs are Fords.
This fact can be
represented by Venn
diagram.
From the Venn diagram, we
can also write an ”if-then”
statement.
If…
Then…
These If-Then statements
are called conditional
statements.
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In logical notation, conditionals are written as
follows:

If p then q
p
Or
q
( read as “p implies q”)
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In conditional, the part following the word if
is the hypothesis. The part following the then
word is the conclusion.
Identify the hypothesis and conclusion:
If a car is a Mustang, then it is a Ford.

Write the statement as a conditional.
Underline the hypothesis and circle the
conclusion. Also draw a Venn diagram for the
statement.
North Thurston HS is in Washington.

Now consider the following statement:
You attend NTHS.
By placing YOU into our Venn diagram, what
can you logically conclude?

When you switch the hypothesis and
conclusion of a conditional statement, you
have the
CONVERSE
of the conditional.
Example:
Write the converse of the conditional
Conditional: If you have a dog, then you have a
pet.
Converse:

When you negate the hypothesis and
conclusion of the conditional statement, you
have the
INVERSE of the conditional.
Example:
Write the inverse of the conditional
Conditional: If you have a dog, then you have a
pet.
Inverse:

When you switch AND negate the hypothesis
and conclusions statement, you have the
CONTRAPOSITIVE of the conditional.
Example:
Write the contrapositive of the conditional
Conditional: If you have a dog, then you have a
pet.

In the previous example, the conditional
statement is true. Are the related conditionals
true?
Converse?
Inverse?
Contrapositive?

How did you know?
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The contrapositive of a true statement is
always TRUE, and the contrapositive of a false
condition is always FALSE.
The converse and inverse of a conditional are
either both TRUE or both FALSE.
An example which proves that a statement is
false is a COUNTEREXAMPLE.
Write the converse, inverse, and contrapositive
for the conditional. Determine if the
statements are true or false. If false, give a
counterexample.
If you are 16 years old, then you are a
teenager.

Conditional statements that can be linked
together are called
LOGICAL CHAINS.
An example of a logical chain is the children’s
series “If you give..”
http://www.graves.k12.ky.us/powerpoints/elementary/winaelliott.ppt

Arrange the following conditionals into a
logical chain.
Given:
1) If there is a parade, then fireworks will go
off.
2) If there is July 4th , then flags are flying.
3) If flags are flying, then there is a parade.
Prove: If there is July 4th, then fireworks will go
off.