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WorksheetsReasoning
Total questions: 33
Worksheet time: 2hrs 15mins
Name
Class
Date
1.
Determine whether the stated conclusion is valid.
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments.
R is the midpoint of QS.
Conclusion: QR=RS
Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments.
R is the midpoint of QS.
Conclusion: QR=RS
a)
Valid
b)
R is the midpoint
c)
Invalid
d)
A point is the midpoint of a segment.
2.
Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
a)
Invalid
b)
Valid
c)
Sammy is a Great Dane
d)
Sammy is really a cat.
3.
Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
a)
Then it's not odd.
b)
Then it's a whole number.
c)
Then its square is divisible by 4
d)
Then it's even.
4.
Draw a conclusion from the statement.
If a parasite lives in or on a host organism, then it harms its host.
A virus is a parasite.
If a parasite lives in or on a host organism, then it harms its host.
A virus is a parasite.
a)
It will harm the host.
b)
I have a cold.
c)
It lives in or on a host
d)
Invalid
5.
Draw a conclusion from the statement.
If you live in Orlando, then you live in Florida.
You live in Orlando.
If you live in Orlando, then you live in Florida.
You live in Orlando.
a)
You live in Disney Land
b)
You are an old person.
c)
You live in Florida
d)
You live in Orlando
6.
Draw a conclusion from the statement.
If you are at least 25 year old, then you can rent a car.
You can rent a car
If you are at least 25 year old, then you can rent a car.
You can rent a car
a)
You are at least 25 years old
b)
You can rent a car
c)
You can go on a road trip
d)
Invalid
7.
Draw a conclusion from the statement.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.
a)
Jack skipped school.
b)
It isn't Monday.
c)
It's Saturday.
d)
Invalid
8.
Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
a)
You have more energy
b)
If you exercise regularly, then you have more energy
c)
You have a healthy body
d)
If you do not have a healthy body, then you do not exercise regularly
9.
(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3) The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
(2) AJ drives safely.
(3) The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
a)
Law of Detachment
b)
Law of Syllogism
c)
Law of Contrapositive
d)
invalid
10.
p→q
q→r
∴p→r
Which law is modeled?
q→r
∴p→r
Which law is modeled?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
Law of Shannon
11.
p→q
p
∴q
Which law is modeled?
p
∴q
Which law is modeled?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
Law of Shannon
12.
(1) If you have a can opener, you can open a can.
(2) Jon has a can opener.
(3) John can open a can.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
(2) Jon has a can opener.
(3) John can open a can.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
a)
Law of Syllogism
b)
Law of Detachment
c)
invalid
13.
If a mineral is gypsum, it has a hardness of 2.
If a mineral has a hardness of 2, it can be scratched with a fingernail.
Using the Law of Syllogism, what logically comes next?
If a mineral has a hardness of 2, it can be scratched with a fingernail.
Using the Law of Syllogism, what logically comes next?
a)
If a mineral can be scratched with a fingernail, then it is gypsum.
b)
If a mineral is gypsum, it can be scratched with a fingernail.
c)
If a mineral has a hardness of 2, then it can't be scratched with anything.
d)
It can be scratched with a fingernail.
14.
If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?
a)
∠A is complementary to ∠B
b)
∠A is acute.
c)
∠A is obtuse.
d)
∠A is 40⁰
15.
(1) If it is a rabbit, then it has long ears.
(2) Peter Cottontail has long ears.
(3) Peter Cottontail is a rabbit.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
(2) Peter Cottontail has long ears.
(3) Peter Cottontail is a rabbit.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
invalid
16.
Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.
a)
Law of Detachment
b)
Law of Contrapositive
c)
Law of Syllogism
d)
Law of Biconditional
17.
What is a valid counterexample for the following statement?
"If an animal is a panther, then it lives in the forest."
"If an animal is a panther, then it lives in the forest."
a)
It lives in a zoo.
b)
No counterexample, this is true.
c)
It lives in an aquarium.
d)
It is a monkey
18.
What is the conclusion made using syllogism:
If it rains on my bike, then it will get rusty.
If it gets rusty, then I can't ride it anymore.
If it rains on my bike, then it will get rusty.
If it gets rusty, then I can't ride it anymore.
a)
If it rains on my bike, then I can ride it.
b)
If it gets rusty, then I can't ride it.
c)
If it rains on my bike, then I can't ride it anymore.
d)
None of the above
19.
Use Law of Syllogism to make a conclusion.
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft2.
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft2.
a)
If the side of a square is 5 ft, then the perimeter is 20 ft.
b)
If the perimeter of a square is 20 ft, then the area is 25 ft2
c)
If the area of a square is 25 ft2, then the side length is 5 ft.
d)
If the are of a square is 25 ft2, then the perimeter is 20 ft.
20.
What is the symbolic notation for the inverse?
a)
p --> q
b)
q --> p
c)
~p --> ~q
d)
~q --> ~p
21.
Which statement is denoted q --> p ?
a)
conditional
b)
converse
c)
inverse
d)
biconditional
22.
What is the hypothesis of the statement:
'If I like Halloween, then I get candy.'
'If I like Halloween, then I get candy.'
a)
If I like Halloween
b)
I like Halloween
c)
Then I get candy
d)
get candy
23.
Write the if-then form of the statement:
Dogs bark.
Dogs bark.
a)
If an animal barks, then it is a dog.
b)
If the animal is a dog, then it barks.
c)
If dogs bark, then it is an animal.
d)
Invalid
24.
If it is morning, then I drink coffee.
If I drink coffee, then I am more awake.
If valid, what can you conclude?
By which law?
If I drink coffee, then I am more awake.
If valid, what can you conclude?
By which law?
a)
If it is morning, then I am more awake. ; detachment
b)
If it is morning, then I am more awake. ';syllogism
c)
I am more awake. ; detachment
d)
I am more awake. ; syllogism
25.
Which are pairs of vertical angles?
a)
∠COB & ∠COA
b)
∠AOD & ∠AOC
c)
∠COB & ∠AOD
d)
∠BOD & ∠AOD
26.
Which are pairs of adjacent angles?
a)
∠COB & ∠DOA
b)
∠AOD & ∠AOC
c)
∠COB & ∠AOD
d)
∠BOD & ∠AOC
27.
If the measure of ∠2 is 83°, what is the measure of ∠3?
a)
7°
b)
17°
c)
83°
d)
97°
28.
Find the value of r?
a)
46
b)
44
c)
43
d)
47
29.
Find the value of t.
a)
-1
b)
5
c)
5.14
d)
7
30.
For the inverse, we _________ the hypothesis and conclusion.
a)
flip
b)
negate
c)
Flip and negate
d)
do nothing to
31.
Which is the correct if-then statement for the statement.
A dog with proper training will not misbehave.
A dog with proper training will not misbehave.
a)
If a dog has proper training, then it will not misbehave.
b)
If a dog does not behave, then it had proper training.
32.
State the inverse:
If I am not happy then no one is happy
If I am not happy then no one is happy
a)
If I am not not happy then, no one is. happy
b)
If I am happy, then no one is not happy.
33.
Conditional: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
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