Chapter 2 2.3 Deductive Reasoning.

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Presentation transcript:

Chapter 2 2.3 Deductive Reasoning

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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?