2A Symbols
2B Counterexamples and Truth Value
2B Conditionals
2C Shading and Creating Venn Diagrams
2C Interpreting Venn Diagrams
100
Given: p\rightarrow q
Write a sentence that represents this logical statement using the following.
p: it is raining
q: the ground is wet
If it is raining, then the ground is wet.
100
Is the following statement true or false?
If a bird is a penguin, then it cannot fly.
True because penguins are birds that cannot fly.
100
Identify whether the new statement is the converse, inverse, or contrapositive of the original.
Original: If it is snowing, then it is cold.
New: If it is cold, then it is snowing.
Converse
100
Shade the following Venn diagram based on the statement below.
People who enjoy the city and the country.
only the middle should be shaded
100
How many people enjoy all 3 - pizza, breadsticks, and soda?
20 people
200
Given: It is not sunny and it is cold.
Translate this statement into logic symbols when
p: it is sunny
q: it is cold
\not p\wedge q
200
Give a counterexample to the following false statement.
If an animal lives in the ocean, then it is a fish.
Dolphins, whales, etc
200
Identify whether the new statement is the converse, inverse, or contrapositive of the original.
Original: If a student passes the final exam, then they pass the course.
New: If a student does not pass the final exam, then they do not pass the course.
Inverse
200
Shade the following Venn diagram based on the statement below.
People who enjoy the city or the country.
both circles including the middle should be shaded
200
How many people only enjoy soda?
0 people
300
Given: The light is on if and only if the switch is not off.
Translate this into logic symbols when
p: the light is on
q: the switch is off
p\leftrightarrow \not q
300
Is the following statement true or false?
If it is New Year's Day, then it is January 1st.
False, many cultures and religions such as Chinese New Year and Rosh Hashanah fall on different dates.
300
Identify whether the new statement is the converse, inverse, or contrapositive of the original.
Original: If a device can access the internet, then it is connected to Wi-Fi.
New: If a device is not connected to Wi-Fi, then it cannot access the internet.
Contrapositive.
300
Shade the following Venn diagram based on the statement below.
People who prefer waffles and pancakes but not eggs.
the middle of waffles and pancakes without the egg circle should be shaded
300
How many people enjoy pizza and breadsticks?
70 people
400
Given: \therefore m \vee n
Translate the symbols into words when
m: it is sunny
n: it is raining
Therefore, it is sunny or it is raining.
400
Is the following statement true or false?
If the current month is December, then the next month is January.
True.
400
Write the contrapositive of the given statement.
If a person is 18 years old, then they can vote in the United States.
If a person cannot vote in the United States, then they are not 18 years old.
400
Create the Venn diagram for the situation below.
20 people were surveyed.
12 people were in an English class.
10 people were in a History class.
2 people were in both classes.
2 people in the middle
10 people in the English
8 people in the History
400
How many people enjoy soda or pizza?
150 people
500
Given: (p\vee q) \rightarrow r
Write a sentence that represents this logical statement using
p: the alarm is set
q: the door is locked
r: the house is secure
If the alarm is set or the door is locked, then the house is secure.
500
Give a counterexample to the following false statement.
If an animal lays eggs, then it is a bird.
Snakes, frogs, etc
500
Turn the following statement into a biconditional.
If a substance is water, then it freezes at 32 degrees.
A substance is water if and only if it freezes at 32 degrees.
500
Create the Venn diagram from the situation.
10 people were surveyed.
4 people prefer to watch movies.
5 people prefer to listen to music.
3 people prefer both.
3 people in the middle
2 people in music
1 person in movies
4 people outside the circles
500
How many people like breadsticks but do not like pizza?
10 people