Cs610 Lecture 1 Symbolic Logic Examples And Worksheet Page 10

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An argument form is valid if the conclusion is always true when
An argument is valid when its argument form is valid.
Here’s an argument you (may have) presented to your parents in high school. Is it valid?
If I have a rock concert on our deck, I am a cool.
I am cool.
∴ I (should/will) have a rock concert on our deck.
p
q
q
p
p →q
If Kelly solved the problem, then Kelly is a genius or Kelly cheated.
Kelly did not cheat, and Kelly solved the problem.
∴ Kelly is a genius.
p
q
r
? Critical
Rows
T
T
T
T
T
F
T
F
T
T
F
F
F
T
T
F
T
F
F
F
T
F
F
F
Two famous rules of inference:
Modus ponens: (method of affirming)
Modus tollens: (method of denying)
p → q
p → q
p
~ q
∴ q
∴ ~ p
Is this argument valid?
If you are a CS major, then you are held in awe by most Loyola students.
You are not held in awe by most Loyola students.
∴ You are not a CS major.
CS610 Lecture 1 p. 10

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