# 5 3 4 | 6 7 8 | 9 1 2 6 7 2 | 1 9 5 | 3 4 8 1 9 8 | 3 4 2 | 5 6 7 -------+-------+------ 8 5 9 | 7 6...

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5 3 4 | 6 7 8 | 9 1 2 6 7 2 | 1 9 5 | 3 4 8 1 9 8 | 3 4 2 | 5 6 7 -------+-------+------ 8 5 9 | 7 6 1 | 4 2 34 2 6 | 8 5 3 | 7 9 17 1 3 | 9 2 4 | 8 5 6 -------+-------+------ 9 6 1 | 5 3 7 | 2 8 4 2 8 7 | 4 1 9 | 6 3 5 3 4 5 | 2 8 6 | 1 7 9

I have one, you have one. If you remove the first letter, a bit remains. If you remove the second, bit still remains. After much trying, you might be able to remove the third one also, but it remains. It dies hard!

Geometric ThinkingInductive Reasoning: making a conclusion based on patterns of examples or past events. Uses examples to arrive at a reasonable generalization or conclusion.EXAMPLE:1. Find the next three terms of the sequence 102, 98, 94, .

2Find the next three terms of the sequence 13, 14, 17, 22, 29, .

3Draw the next figure in the pattern.

Conjecture: a conclusion you reach based on inductive reasoning. An educated guess.To prove a conjecture TRUE, it must always be true.

To prove a conjecture false, you need to show only ONE counterexample.

EXAMPLEGive a counterexample for the statement ''All fruits taste sweet''

True or False1. Someone paid $14,000 for the bra worn by Marilyn Monroe in the film 'Some Like It Hot'. 2. Your tongue is the only muscle in your body that is attached at only one end. 3. More than 1,000 different languages are spoken on the continent of Africa. 4. A kiss lasting one minute can burn more than 100 calories. 5. The Bible, the world's best-selling book, is also the world's most shoplifted book.6. Buckingham Palace in England has over six hundred rooms. 7. There was once an undersea post office in the Bahamas. 8. Abraham Lincoln's mother died when she drank the milk of a cow that grazed on poisonous snakeroot. 9. After the death of Albert Einstein his brain was removed by a pathologist and put in a jar for future study.

taken fromhttp://www.world-english.org/facts_true.htmThe 1 minute kiss only burns 30 calories.

StatementsA statement is either true or false, but not both. The truth value shows the truth or falsity of a statement.The joining of two or more statements is a compound statement.1) Conjunction: joining two or more statements with and (symbol ). To be true, both statements must be true. Notation pq2) Disjunction: joining two or more statements with or (symbol ). To be true, only one statement must be true. Notation pq

Negation of a statementThe negative or opposite of a statementSaidnot pSymbol ~

Example: p = It is cloudy today~p = It is not cloudy today.

Truth Valuesp: One foot is 14 inchesq: October has 31 daysr: A plane is defined by 3 non-collinear points

Evaluate:p qp r~p qr q~p ~q

Entrance Slip 9-28

5.

Conditional StatementsConditional Statement: a statement written in if, then form.

EX: If it is cloudy, then it will rain.

The if part is called the hypothesis and the then part is called the conclusion.

It is an implication relationship!!!

SymbolsWordsConditionalpqIf I study hard, then I will ace the test.ConverseqpIf I aced the test, then I studied hardInverse~p~qIf I do not study hard, then I will not ace the test.Contrapositive~q~pIf I did not ace the test, then I did not study hard

Write theof the following statement

converse:

inverse:

contrapositive:

Write the converse of

Write the contrapositive of

Write the converse of

Write the inverse of

Write the contrapositive of

Write the inverse of

Write the converse of

Write the contrapositive of

Write the inverse of

Write the contrapositive of

Part I ~ SequencesPart II ~ Conjecture

Part III ~ Compound Statements

Part IV ~ Conditional StatementsWrite the inverse of the first statement.Write the contrapositive of the second statement.Write the converse of the second statement.

Part V ~ Venn Diagrams

Deductive Reasoningusing facts, rules, properties & definitions to reach a logical conclusion.

Deductive ReasoningDefinitionSymbolsLaw of Detachmentpq is true and p is true: q is true [(pq)p]q Law of SyllogismIf pq and qr are true: then pr is true [(pq)(qr)](pr)

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