Cs610 Lecture 1 Symbolic Logic Examples And Worksheet Page 11
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12Is this argument valid?
If you are a CS major or you are a math major, then you are held in awe by
Can a valid
most Loyola students.
argument have a
You are a math major or you are a CS major.
false conclusion?
∴ You are held in awe by most Loyola students.
p
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Contradiction Rule:
~p → c
If you are not tall, then the sky is blue and the sky is not blue.
∴ p
p
~p
c
p
~p →c
Proof by Contradiction
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the
truth and knaves who always lie. You visit the island and are approached by two natives who speak to you as
follows:
A says: B is a knight.
B says: A and I are of opposite type.
What are A and B?
Suppose A is a knight.
_______________________
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Fallacy = error in reasoning that results in an invalid argument
Converse error: based on the assumption that the
of the argument would follow from
the premises if the premise p → q where replaced by its converse.
ex:
If you are a nerd, you are a CS major.
You are a CS major.
∴ You are a nerd.
CS610 Lecture 1 p. 11
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