#1
Sketch the next figure in the pattern.
1.
2.
3.
Write the next number in the sequence.
4. 0, 1, 3, 6, 10, 15, 21, …
5. 2, 1, 0.5, 0.25, …
6. 1, 2, 4, 8, 16, …
7. 3, –3.3, 3.33, –3.333, …
#2
Determine whether each statement below is the converse, inverse, or contrapositive of the original statement.
1.
Original statement / If the weather is rainy, then it’s pouring.? / If the weather is not rainy, then it’s not pouring.
2.
Original statement / If something has peanuts, then I can’t eat it.? / If I can eat something, then it doesn’t have peanuts.
3.
Original statement / If I hear music, then I dance.? / If I dance, then I hear music.
4.
Original statement / If I got at least a 70%, then I passed.? / If I did not pass, then I did not get at least a 70%.
5.
Original statement / If x = 4, then 3x + 7 = 19.? / If 3x + 7 = 19, then x = 4.
6.
Original statement / If I am sick, then I will not go to school.? / If I go to school, then I am not sick.
#3
Give a counterexample for each of the following statements.
1. Every month has 31 days.
2. All integers greater than –2 must be positive.
3. All athletes play soccer.
4. If the sum of two number is positive, then both numbers must be positive.
Fill in the blank.
5. A biconditional statement must contain the phrase ______.
6. The ______of a statement means to switch the hypothesis and conclusion.
7. An ______statement contains a hypothesis and a conclusion.
8. The ______of a statement means to switch and negate the hypothesis and conclusion.
9. The ______of a statement means to negate the hypothesis and conclusion.
#4
Use the following two statements to answer each question.
If there is a full moon, then Mitch will turn into a werewolf. If Mitch turns into a werewolf, then he will have yellow eyes.
1. What statement would follow?
A – Mitch turned into a werewolf.
B – Mitch has yellow eyes.
C – If Mitch has yellow eyes, then there is a full moon.
D – If there is a full moon, then Mitch has yellow eyes.
2. Which law was used?
A – Law of Detachment
B – Law of Syllogism
Use the following two statements to answer each question.
If Virginia Tech wins a football game then Mrs. Schutte will be very happy. Virginia Tech beat Nebraska.
3. What statement would follow?
A – Nebraska fans were happy.
B – Mrs. Schutte is very happy.
C – If Virginia Tech wins a football game, then they played Nebraska.
D – If Mrs. Schutte is very happy, then Virginia Tech won a football game.
4. Which law was used?
A – Law of Detachment
B – Law of Syllogism
Use the following two statements to answer each question.
If a college football team loses to Duke then they 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
#5
Given the following statement, write the if-then, converse, inverse, and contrapositive.
1. There is sand under your feet if you are standing on the beach.
Given the two following statements are true, write a biconditional statement.
2. If someone is a realtor, then they sell houses.
If someone sells houses, then they are a realtor.
#6
Use the Venn diagram to fill in the blank with the correct quantifier – “all”, “some”, or “no”
People who live in the USA 1. _____ people who live in Ohio live in the USA
People who live 2. _____ people who live
in Ohio. in the USA live in Ohio
Use the Venn diagram to fill in the blank with the correct quantifier – “all”, “some”, or “no”
1. _____ XC runners are also soccer players
2. _____ soccer players are athletes
3. _____ athletes are XC runners
4. _____ guitar players are athletes