Geometry –
Name
____________
Unit 1, Day 5 Warm Up
1. If you decide to go to the soccer game, then you will miss baseball practice.
You go to the soccer game. What can you conclude?
You will miss baseball.
2. Write a true statement that follows the pair of statements.
If Lindsay goes to college, then she will major in Chemistry.
If Lindsay majors in Chemistry, then she will need to buy a lab manual.
If Lindsay goes to college, then she will need to
buy a lab manual.
3. Determine the next two numbers.
a. 2, 4, 7, 11, 16, …
b. –48, 24, –12, 6, …
-3, 1.5
22, 29
4. Use the given information to draw a Venn
a.
Some fish are yellow.
b.
Some fish are yellow and blue.
All fish live in water.
Live in
Water
fish
Blue
Yellow
diagram.
Some football players run track.
Some cheerleaders run track.
No football players are cheerleaders.
Cheerleaders
Track
Football
Chapter 2 Study Guide
Name _____________________
Date ______________________
Section 2.1 Inductive Reasoning:
An unproven statement that is based on observations is a ____________.
conjecture
A process that includes looking for patterns and making conjectures is called
_______________
Inductive______________________.
reasoning
A specific case that shows a conjecture is false is a ____________________________.
counterexample
Sketch the next figure in the pattern:
1)
Write in the next number in the sequence:
2)
3)
0, 1, 3, 6, 10, 15, 21, 28, 36, 45,
4)
3, -3.3, 3.33, -3.333, 3.3333
Give a counter example to each of the following statements: Answers
5) Everyone in this classroom is a student.
8) All months have either 30 or 31 days.
-3.33333
may vary
Ms. Gallagher is in the classroom
6) Each person has a birthday once each year. True
7) All integers greater than –2 are positive.
55
statement (no counterexample)
-1 is greater than -2
February has 28 days
Section 2.2 Conditional Statements
SYMBOLIC NOTATION
p ____________
hypothesis
Conditional Statements A logical argument that has two parts,
q
_____________
conclusion
hypothesis
conclusion
a ______________________
and a ___________________
Converse:
“if p then q”
switch
_______________
the hypothesis and conclusion
negate
Inverse: ___________________
the hypothesis and conclusion
switch
Contrapositive: ______________
and ________________
the
negate
hypothesis and conclusion
SPECIAL CASES
A statement can be written as a bi-conditional statement if and only if it the
conditional and its _______________________are
converse
________________
____________.
true
When two statements are both true or both false, they are called
________________________________.
Examples: Conditional and Contrapositive
Equivalent statements
statements. Converse and Inverse statements
9) Write each of the following statements as a conditional statement.
If you tell the truth, then you don’t have to remember anything.
If you go to bed early and get up early, then you will be healthy,
wealthy, and wise.
Label each of the statements below as either the converse, inverse, or contrapositive of the original
statement:
10)
Original Statement:
? inverse
11)
If it does not rain then it does not pour.
Original Statement:
If food has peanuts, then I can’t eat it.
? contrapositive If I can eat food, then it does not have peanuts
12)
Original Statement:
?converse
If I hear music then I dance.
If I dance then I hear music.
13)
Original Statement:
?contrapositive
If I got at least 70% of the questions right, then I passed.
If I didn’t pass, then I got less than 70% of the questions right.
14)
Original Statement:
?biconditional
If Mrs. Wright smiles, then you smile.
Mrs. Wright smiles if and only if you smile.
2.3 Deductive Reasoning
Using facts, definitions, accepted properties, and the laws of logic to form a logical argument is called
Deductive reasoning
____________________________________
LAWS OF LOGIC
Law of Detachment:
Conditional statement is true and a statement is
A conclusion can be made when a ________________________________
made based on the hypothesis of that conditional statement.
Example: If I study for my test, then I will get a good grade. I study for my test.
Conclusion: Then I will get a good grade.
Conditional statement is true and a statement is
A conclusion is not possible when a _________________________________
made based on the conclusion of that conditional statement.
Example: If I study for my test, then I will get a good grade. I get a good grade.
This has no conclusion.
Law of Syllogism:
Given the following pattern
If hypothesis, p, then conclusion, q
If hypothesis, q, then conclusion, r
Then following statement can be made
If hypothesis p, then conclusion r.
2.3 Deductive Reasoning (con’t)
Given the following two statements:
If there is a full moon then Vince will turn into a werewolf. If Vince turns into a werewolf then he will
play with the ball of yarn.
15) What statement would follow?
A – Vince turned into a werewolf.
B – Vince played with a ball of yarn.
C – If Vince plays with a ball of yarn then there is a full moon.
D – If there is a full moon then Vince will play with a ball of yarn.
16) Which law was used?
A – Law of Detachment
B – Law of Syllogism
Given the following two statements:
If the New England Patriots loose a football game, then Mrs. Clark will be very sad. Mrs. Clark is very
sad.
3) What statement would follow?
A – The Patriots lost to the Cowboys.
B – No conclusion.
C – If the Patriots loose a football game, then they played the Redskins.
D – If Mrs. Clark is very sad, then New England lost a football game.
4) Which law was used?
A – Law of Detachment
B – Law of Syllogism
Given the following two statements:
If a college football team losses to Duke then it must be terrible. UVA’s football team lost to Duke.
5) What statement would follow?
A – UVA has a terrible football team.
B – Virginia Tech is a great football team.
C – If UVA loses then Duke is a good team.
D – If a college football team loses then it must be UVA that lost.
6) Which law was used?
A – Law of Detachment
B – Law of Syllogism
Inductive or Deductive Reasoning Check
Decide whether Mr. Pibb reaches his conclusion using inductive or deductive reasoning:
1) Mr. Pibb drives 75 mph on a road where the speed limit is 55. So Mr. Pibb believes he is breaking
the speed limit.
inductive
2) Mr. Pibb knows that there has been a speed trap up ahead every day for the past month. So Mr.
Pibb decides to slow down.
inductive
3) Mr. Pibb decides to eat lunch fast food restaurant. He thinks about going to Taco Bell but every
time he has eaten there, he gets really bad heartburn. So Mr. Pibb decides to eat somewhere else.
deductive
4) Mr. Pibb goes to McDonalds where he chooses value meal #1. Since value meal #1 costs $5.45
with tax, Mr. Pibb decides he should get out six dollars so that he will have enough money to pay for
his lunch.
deductive
Venn Diagrams
1 – In which region would you
find hamburgers?
I
2 – In which region would you
find chicken nuggets?
IV
3 – In which region would you
find soda? VII
According to the diagram, fill
in blanks using all, some, or none:
All cat are animals and ______
Some
4. ____
animals are cats.
No Flying Monkeys are
5. _____
animals and ______
No animals are
Flying Monekys.
Symbolic Notation Summary
Elephants fly
Fish don’t swim
Elephants don’t fly
Fish Swim
If fish don’t swim, then elephants fly.
If elephants don’t fly, then fish swim.
If fish swim, then elephants don’t fly.
Therefore elephants fly.
Elephants fly if and only if fish
don’t swim.
p→q
q→p
~p → ~q
~q → ~p