1. Chapter 2 2.3
Deductive Reasoning

2. Determine what follows from these two statements
If I have reached the party to whom I am speaking, then I have dialed correctly
I have indeed reached the party to whom I am speaking
If the Jolly Green Giant started turning blue, he should put on a sweater
The Jolly Green Giant has not started turning blue

3. Determine what follows from these two statements
If you see spots in front of your eyes, then you are looking at a leopard
You’re looking at a leopard
If you forgot your pencil, then you may borrow one of mine.
You forgot your pencil

4. Symbolic Notation Conditional: If a then b
Conditional Symbolized: a  b
In English we would say “a implies b”
Example: If the sun is out then the weather is good
the sun is out  the weather is good
s  g

5. Symbolic Notation Biconditional: a if and only if b
Biconditional Symbolized: a  b
In English we would say “a if and only if b”
Example: The sun is out if and only if the weather is good
The sun is out  The weather is good
s  g

6. Symbolic Notation Negation: not Negation Symbolized: ~
Example: The sun is out
Negation: The sun is not out
Symbolized: ~s

7. Write the symbolic statement in words p: The value of x is 4
Write the symbolic statement in words p: The value of x is 4 q: 3x + 2 = 14 ~p ~q
q  p

8. Write the symbolic statement in words p: The value of x is 4
Write the symbolic statement in words p: The value of x is 4 q: 3x + 2 = 14
~q  ~p
p  q
~p  ~q

9. Determine what follows from these two statements
If an angles measures more than 90 then it is not acute.
MABC = 120
If you order apple pie, then it will be served with ice cream.
Matthew ordered apple pie

10. Determine what follows from these two statements
If you wear school colors, then you have school spirit.
If you have school spirit, then the team feels great.
If you eat to much turkey then you will get sick
Kinsley got sick

11. The law of detachment
If p  q is a true conditional statement and p is true , then q is true
If the class is boring, then the students will stop paying attention
The class is boring
The student are not paying attention

12. The law of syllogism
If p  q and q  r then p  r is a true conditional statement
If  2 is acute, then  3 is obtuse
If  3 is obtuse, then  4 is acute
If , then

13. Determine what follows from these two statements
13. All 45 angles are 
A   B
Counter example:

14. Conditional Statement
More Symbolism
Equivalent statements
Conditional Statement
p  r
Contrapositive
~r  ~p
Example
If the car will start, then the battery is charged
If the battery is not charged, then the car will not start

15. More Symbolism Equivalent statements Converse r  p Inverse ~p  ~r
Example
If the battery is charged, then the car will start
If the car will not start, then the battery is not charged

16. If Susan screams then the dog will run away If the dog licks Susan, then Susan will scream If Carl tells the dog to “kiss”, then the dog will lick Susan Carl tells the dog to “kiss”.
Contapositive of #3 14. Inverse of #2 15. Converse of #1 16.

17. If Susan screams then the dog will run away If the dog licks Susan, then Susan will scream If Carl tells the dog to “kiss”, then the dog will lick Susan Carl tells the dog to “kiss”.
16. Appropriate Order? 17. Did the dog lick Susan? 18. Did the dog run away?