Mrs Skaff Symbol In Words Meaning p q or r Symbol In Words Meaning p q or r What is Logic Logic is a way to describe situations or knowledge that enables us to reason from existing knowledge to new conclusions ID: 781202
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Slide1
Logic
Math Studies IB
NPHS
Mrs. Skaff
Slide2Symbol
In WordsMeaningp, q, or r¬
Symbol
In Words
Meaning
p, q,
or
r
¬
Slide3What is Logic?
Logic is a way to describe situations or knowledge that enables us to reason from existing knowledge to new conclusions. For example:All college students are poorI am college a studentTherefore, I am poor If the original statement is false, the conclusion is still logical (it just may be false)All college students are rich (not true)I am a college studentTherefore, I am rich!
Slide4Logical Reasoning
You have four cards. A letter A – Z is the blue side. A number 0 – 9 is on the green side. You have these cards:EK47What card do you turn over to test the rule “If a card has a vowel on the blue side, it must have an even number on the greenside? 5
Slide5Sets and Logical Reasoning
A proposition is a statement that may be true or false.For Example,“Mrs. Skaff is a math teacher” is a true proposition“Mrs. Skaff is 10 feet tall” is a false proposition“Today is Saturday” is indeterminate because it may be true of false depending on the circumstances.All of these are examples of simple propositions.
Slide6Propositions
Consider the following statements:Go get the bookHave you seen my new shirt?The dog is behind the shedWhich statement is a proposition?The dog is behind the shed.Rewrite the others so they are propositionsSiya got the book.Jackson saw my new shirt.
Slide7Representing propositions
We represent propositions by letters such as p, q, and r.For Example:p: Mrs. Skaff is a math teacherq: Mrs. Skaff is 10ft tallr: Today is SundayOpposites are represented by negation (¬)¬p represents the opposite of pWe read that as “not p”¬p: Mrs. Skaff is not a math teacher¬q: Mrs. Skaff is not 10ft tall¬r: Today is not Sunday
Slide8Compound Propositions
Compound propositions are statements which are joined using and or or. ConjunctionsWhen two propositions are joined using and the new proposition is the conjunction of the originals.The conjunction of the two propositions p and q is denoted by pq
Slide9Truth Values
Because a proposition is a statement that can be either true or false, its Truth Values are T for true and F for false. This may be represented in a table.p : Carla has black hair¬ p : Carla does not have black hairTF
Slide10Conjunctions
For the following propositions:p: Ty is a superheroq: Sofia is a basketball starWhat is p^q : Ty is a superhero and Sofia is a basketball star What is ¬p^q Ty is not a superhero and Sofia is a basketball star
Slide11Conjunction: Truth Value
The truth value of a conjunction is only true with BOTH the propositions are true. pqpqTTTFFTFFpqTTTFF
T
F
F
Slide12Conjunctions: Truth Value
p: Mrs. Skaff is a math teacherq: Mrs. Skaff is 10ft tallr: Today is SundayFind the truth value of pq pqpqTTTTFFFTFFFFpqTTTTFF
F
T
F
F
F
F
Slide13Simple Truth Table
pq¬qp¬qTTFFTFTTFTFFFFTFpq¬q
T
T
F
F
T
F
T
T
F
T
F
F
F
F
T
F
Find the truth value of p^
¬
q
Slide14Disjunctions
A disjunction is formed when propositions are joined using the word “or” This is written as p qThe truth value of a disjunction is true when at least one of the propositions is true. pqp qTTTTFTFTTFFFpqTTTTFT
F
T
T
F
F
F
Slide15Disjunction
Example: Find the disjunction between the two propositionsp: Pikachu is a Pokemonq: Mrs. Dogancay is a Pokemonp is true (Mrs. Skaff’s favorite pokemon!)q is not true (unless there is something Mrs. Dogancay is hiding from us)THEREFORE, p q is true. pqp ∨ qTTTTFTFTTFFF
Slide16Exclusive Disjunction
Chandler will go home if John is running late or if it is raining. You will go to Hawaii by boat or by plane.In the first, Chandler will go home if John is late, it’s raning, or bothIn the second, you can travel by boat or plane, but not both at the same time.Thi is called an exclusive disjunctionp q pqp qTTFTFTFTTFFFpqTTFTFT
F
T
T
F
F
F
Slide17Venn Diagrams
You will go to Hawaii by boat or by planep: you will go by boatq: you will go by planeplaneboat
Slide18Practice
p: London is the capital of England q: 45 – 5 = 4 r: Cows have 4 legsFind the truth value of the following:p ^ qq v r¬q ^ r¬(p v q)p v r FalseTrueTrueFalseFalse