Chapter 2.1-2.2 Logic. Conjecture 4 A conjecture is an educated guess. 4 Example: If you walk into a DRHS classroom where the teacher is speaking Spanish,

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Presentation transcript:

Chapter Logic

Conjecture 4 A conjecture is an educated guess. 4 Example: If you walk into a DRHS classroom where the teacher is speaking Spanish, there are Spanish posters on the walls and Spanish words on the board, you would conjecture that you were in a Spanish class.

Inductive vs. Deductive reasoning 4 Inductive: take known information make conjectures (good guesses) 4 Deductive: formally prove through a series of reasons that a statement is true

Examples 4 Inductive: It is cloudy outside 4 Inductive Math: The sum of two angles is 180 o Conjecture: It will rain today Conjecture: They are supplementary

If-Then Statements (Conditional Statements) 4 Follow a pattern: –If (state the hypothesis) then (state the conclusion) 4 Ex: If I do my homework, then I will succeed –Hypothesis: I do my homework –Conclusions: I will succeed

Examples Turn each into an If-then statement 1) A cat sheds hair -If an animal is a cat then it sheds hair 2) A cow cannot be tipped -If an animal is a cow, then it cannot be tipped.

FOUR FUNDAMENTAL STATEMENTS!!! 4 P: HypothesisQ: Conclusion 4 ~: means “not” or the opposite of the given statement 4 means “therefore” 1. Conditional: P  Q 2. Converse: Q  P 3. Inverse: ~P  ~Q 4. Contrapositive: ~Q  ~P

Write the given statement in each way 4 Conditional: If I make an A, then I pass the test 4 Converse: If I pass the test, then I make an A 4 Inverse: If I don’t make an A, then I won’t pass the test 4 Contrapositive: If I don’t pass the test, then I won’t make an A

VERY VERY IMPORTANT!!! 4 The inverse and converse may not be true!! 4 The contrapositive is always true if the conditional is true

Venn diagrams: 4 show relationships between different sets of data. 4 can represent conditional statements.

A Venn diagram is usually drawn as a circle. 4 Every point IN the circle belongs to that set. 4 Every point OUT of the circle does not. A=poodle... a dog B= horse... NOT a dog. B DOGS.A.A...B   dog

For all..., every..., if...then... rose Every rose is a flower. flower

4 Every cow is a mammal Mammals cows

Perpendicular 4 When 2 lines are perpendicular, they form 90 degree angles. 4 We use this sign:

Counter-example 4 Is an example that proves a statement false. (It can be a picture!) 4 Ex. “Every set of three points can be connected to form a triangle.” the counter- example is: 4 (You cannot form a triangle from these points because they just form 1 line)