Geometry
Notes
Name_______________________________
Date _________________ Pd ___________
WARM UP, Unit 1, Day 4
1. If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true
statements.
If Tim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Tim gets stung by a
bee.
2. If possible, use the Law of Detachment to make a valid conclusion given the following statements.
If you drive 50 miles per hour in a school zone, then you will get a speeding ticket. Pat received a speeding ticket.
3. Use p as “you don’t eat meat” and q as “you are a vegetarian”
a) Show the symbolic notation and write the statement.
Conditional-
Converse –
Inverse –
Contrapositive –
b) Using the conditional statements above, write the bi-conditional statement if possible.
Today:
 You will learn how to use Venn Diagrams to represent set relationships.
 At the end of class you will be able to interpret Venn Diagrams and answer questions about the related sets.
You will also be able to draw simple Venn Diagrams given information about the relationships between sets.
You will understand how to use set notation.
Venn Diagrams
Venn diagrams ___________________________________________________________________. Study the
examples below.
Scenario 1
_____ of the members of A
are also members of B.
Some of the members of B
are also members of A.
Scenario 2
___________ of the members of A
are also members of B.
(and vice versa)
B
B
Scenario 3
______ members of A are
members of B.
(and vice versa)
A
B
A
Example 1
Use the Venn diagram to fill in the blank with the correct quantifier – “all”, “no”, or “some.”
1. __________ cloudy days are rainy days.
Cloudy days
rainy
days
2. __________ rainy days are cloudy days.
Example 2
Use the Venn diagram to fill in the blank with the correct quantifier – “all”, “no”, or “some.”
people
who go
to the
beach
1. __________ students don’t go to the beach.
students
2. __________ people who go to the beach are
students.
Example 3
Use the Venn diagram to fill in the blank with the correct quantifier – “all”, “no”, or “some.”
angles
right
obtuse
1. __________ right angles are obtuse angles.
2. __________ obtuse angles are right angles.
A
Example 4
The Venn diagram illustrates how many students purchased different items during a single lunch shift. Use this
information to answer the following questions.
chips
sandwich
1. How many items were sold altogether?
52
97
33
2. How many sandwiches were sold?
8
27
16
38
milk
Example 5
Draw a Venn diagram using the given information.
Some bicycles are blue.
Example 6
Draw a Venn diagram using the given information.
All fish swim.
Example 7
Draw a Venn diagram using the given information.
Some people drink Pepsi.
Some people drink Coke.
Some people drink Pepsi and Coke!
3. How many students had chips and
milk?
4. How many students had a sandwich,
chips, and milk?
Venn Diagrams And Set Notation
Union – _______ - everything that is in either set
A
B ___________
B
A
Intersection - __________ - Only the things that are in both sets
A
B ____________
A
B
Example 8
The Venn diagram illustrates how many students purchased different items during a single lunch shift. Use this
information to answer the following questions.
1. sandwich
chips
Write in words:
chips
sandwich
52
97
33
What is the value?
8
27
16
2. chips
milk
Write in words:
sandwich
38
milk
What is the value?
3. sandwich
Write in words:
What is the value?
chips