Term
SECTION 2.1-An introduction to Proofs
What is a proof? |
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Definition
A convincing argument that something is true.
Ex: 1. 5X+4=24 2. 5+4=9
-4 -4
5X=20
X=4
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Term
SECTION 2.2- An Introduction to Logic
Euler Diagrams are often called Venn Diagrams
What is a conditional? |
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Definition
A conditional is an "If-Then" statement
Written in form If p then q or p => q (Reads as "P implies q"
Words after If is called the hypothesis, words after then is called the conlusion.
Ex: If a car is a Corvette, then it is a Chevrolet. |
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Definition
Couldn't find pictures compatible with this website so I will explain it instead
Conditional: If a car is a Corvette, then it is a Chevrolet.
Chevrolet would go in rectangle and Corvettewould go into circle because Corvette is a subset of the universal set which is Chevrolets. |
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Definition
Conditional: If a car is a Corvette, then it is a Chevrolet
Converse: If a car is a Chevrolet, then it is a Corvette
Conditional is true,but Converse is false.
When Converse is false, you need to provide a counterexample or an example that proves that the statement is false.
Counterexample: Chevrolet Malibu |
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Term
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Definition
When Conditionals are linked together, they form a logical chain.
If it is winter, then it is December,
If it is snowing, then it cold,
If it is December, then it is snowing.
Conditional: If it is winter, then it is cold.
Conditional = first hypothesis and last conclusion |
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Term
SECTION 2.3-Definitions
How can a conditional be a definition? |
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Definition
If conditional and converse are true, then this is a defintion
Two true conditionals can be combined with "if and only if" (iff)or p<=>q
"if and only if"-biconditional |
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Term
| What is a vertical angle? |
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Definition
| The opposite angle formed by two intersecting lines |
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Term
SECTION 12.1-Truth & Validity in Logic Arguments
Valid Arguments |
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Definition
Premises: statements that come before conclusion
Valid argument equals if premises are all true then conclusion is true.
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Term
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Definition
Modus Ponens (proposing mode)- If p then q, p therefore q
Modus Tollens (Removing mode)- If p then q, not q, therefore not p.
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Term
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Definition
Premises are true,but conditional is false
Forms- 1. Affirming the Consequent
If p then q, q therefore p
2. Denying the Antecedent
If p then q, not p therefore not q |
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Term
SECTION 12.2-AND,OR, and Not in Logic
What is a conjunction? |
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Definition
p: Today is Saturday p q p and q
q: It is the weekend T T T
T F F
F T F
Conjunction-and F F F
Today is Saturday and It is the weekend
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Term
SECTION 12.2
What is a disjunction? |
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Definition
Disjuction-or
Exclusive or-"one or the other"
Inclusive or-"one or the other or both"
p q p OR q
T T T
T F T
F T T
F F F |
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Term
SECTION 12.2
What is a negation? |
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Definition
Adding not to the "p" of a statement
Ex: It is raining outside. => It is not raining outside
p not p
T F
F T
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Term
| SECTION 12.3- Truth Tables |
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Definition
Conditional: If you mow the lawn, then you will get $10
p q p => q
T T T
T F F
F T T
F F T |
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Definition
Conditional: If Little Jimmy lives in Maryland, then he lives in the United States
If Little Jimmy lives in the United States, then he lives in Maryland p q q => p
T T T
T F T
F T F
F F T
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Term
SECTION 12.3
Inverse- Truth Table |
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Definition
Inverse-formed by negating hypothesis and conclusion
p q not p notq not p => not q
T T F F T
T F F T T
F T T F F
F F T T T |
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Term
| Contrapositive-Truth Table |
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Definition
Contrapositive- switching p and q then negating each
p q not q not p not q => not p
T T F F T
T F T F F
F T F T T
F F T T T |
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Term
SECTION 12.4
Contradiction |
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Definition
p AND notq
Proof by Contradiction- To prove a statement is tru,e assume that is it false and show that this leads to a contradiction. |
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