• 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 3• 4 2 6 | 8 5 3 | 7 9 1• 7 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 Thinking
Inductive 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, ….
1 2 Find the next three terms of the sequence 13, 14, 17, 22, 29, ….
2 3 Draw 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.
EXAMPLE
Give 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 from…http://www.world-english.org/facts_true.htm
The 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 pq
• 2) Disjunction: joining two or more statements with “or” (symbol “”). To be true, only one statement must be true. Notation pq
• Negation of a statement– The negative or opposite of a statement– Said…”not p”– Symbol “~”
Example: p = It is cloudy today
~p = It is not cloudy today.
Truth Valuesp: One foot is 14 inches
q: October has 31 days
r: A plane is defined by 3 non-collinear points
Evaluate:
1) p q2) p r3) ~p q4) r q5) ~p ~q
Entrance Slip 9-28
5.
Conditional Statements
• Conditional 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!!!
Symbols Words
Conditional pqIf I study hard, then I will ace the test.
Converse qp If I aced the test, then I studied hard
Inverse ~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 the…of 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 ~ Sequences
Part II ~ Conjecture
Part III ~ Compound Statements
Part IV ~ Conditional Statements
Write 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 Reasoning• using facts, rules, properties & definitions
to reach a logical conclusion. Deductive Reasoning
Definition Symbols
Law of Detachment
pq is true and p is true: q is true
[(pq)p]q
Law of Syllogism
If pq and qr are true: then pr is true
[(pq)(qr)](pr)
