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In
logic, a conditional is a compound
statement formed by combining two sentences (or facts) using the
words "if ... then."
A conditional can also be called an implication. |
The truth values for
a conditional (implication) are hard to remember.
You will want to
study this section.
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The
example below may help you remember the truth values for the conditional: |
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The
statement: |
Your teacher
tells you that "if you participate in class, then you will get
extra points."
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fact
1: "you participate in class."
fact
2: "you get participation points." |
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When is the teacher's statement
true?
1. If you participate
in class (fact 1 true) and you get extra
points (fact 2 true)
then the teacher's statement
is true.
2. If you participate in
class (fact 1 true) and you do not get extra
points
(fact
2 false), then the
teacher did not tell the truth and the statement is false.
3. If you do not participate
in class (fact 1 false), we cannot judge the truth
of the teacher's statement. The teacher did not tell you what would
happen
if you did NOT participate in class. Since we cannot accuse
the teacher of
making a false statement, we assign "true"
to the statement.
"If you
participate in class, then you will get extra points."
will be true in all cases except one:
when you participate in
class and you do NOT get the extra points.
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Mathematicians
often use symbols and tables to represent concepts in logic.
The use of these variables, symbols and tables creates a shorthand
method for discussing logical sentences.
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Truth
table for conditional (if...then):
(notice the
symbol used for "if...then" in the table below)
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A
truth table is a pictorial
representation of all of the possible outcomes of the
truth value of a compound sentence. Letters such as  and 
are used to represent the facts (or sentences) within the
compound sentence. |
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REMEMBER:
IF...THEN is
only FALSE when
T implies F.
All other cases are TRUE. |
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