1. Premise: If it’s a school day, then I have Geometry class.
Case 1: Given: It is a school day
Case 2: Given: I do not have Geometry today.
Case 3: Given: If I have Geometry class, then I will need to stay awake.

2. It is a school day OR it is the weekend.
Given: It is not the weekend.

3. Deductive Reasoning: Drawing Conclusions from Conditionals.
If p then q.
Law of Detachment
If p is true, then q is true.
p q p
_________
∴ q

4. Conditional 1:
If you drive at 3:30 you will encounter a lot of traffic.
Conditional 2:
If you encounter a lot of traffic you will be late for work.
Suppose you drive at 3:30, then what?

5. are true (valid) statements Then we conclude, If p then r
Law of Syllogism If
If p then q and If q then r
are true (valid) statements
Then we conclude,
If p then r
p q
q r
_________
∴ p r

6. If you flunk the test, then you will not graduate.
Suppose you will graduate.
Contrapositive
(Indirect Argument)
p q
not q
_________
∴ not p

7. Conditional: Put your coat on or you will freeze.
Statement: You don’t put your coat on.

8. OR conditionals Statement: Given p or q.
If one is false the other must be true.
p or q
not p
∴ q

9. ∴ not p p q p _________ p q not q _________ p or q not p ∴ q p q q r
Direct Argument
(Law of Detachment)
Indirect Argument
(contrapositive)
p q p
_________
∴ q
p q
not q
_________
∴ not p
Syllogism
OR argument
p or q
not p
∴ q
p q
q r
_________
∴ p r