Quiz about Law of Syllogism/ Detachment

Question 1

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.

Accepted Answer

Valid

Answer

Invalid

Answer

Sammy is a Great Dane

Answer

Sammy is really a cat.

Question 2

Draw a conclusion from the statement.
If you live in Orlando, then you live in Florida.
You live in Orlando.

Accepted Answer

You live in Florida

Answer

You live in Disney Land

Answer

You are an old person.

Answer

You live in Orlando

Question 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.

Accepted Answer

Then its square is divisible by 4

Answer

Then it's not odd.

Answer

Then it's a whole number.

Answer

Then it's even.

Question 4

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

Accepted Answer

Invalid

Answer

You are at least 25 years old

Answer

You can rent a car

Answer

You can go on a road trip

Question 5

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam

Accepted Answer

not possible

Answer

I study for 1 hour each day.

Answer

I do not study for 1 hour each day

Answer

If I do well on the exam, I studied for 1 hour each day.

Question 6

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

Accepted Answer

Valid

Answer

R is the midpoint

Answer

Invalid

Answer

A point is the midpoint of a segment.

Question 7

Draw a conclusion from the statement.
If you go fishing, then you will need to bring your fishing rod.
You go fishing.

Accepted Answer

You will need to bring your fishing rod.

Answer

Invalid

Answer

You are a boring person.

Answer

You are going to catch a fish.

Question 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

Accepted Answer

If you exercise regularly, then you have more energy

Answer

You have more energy

Answer

You have a healthy body

Answer

If you do not have a healthy body, then you do not exercise regularly

Question 9

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

Accepted Answer

If the sun is shining then we will go hiking.

Answer

If the sun is not shining, we will not go hiking.

Answer

No conclusion can be made.

Answer

If we go hiking, then it is a beautiful day.

Question 10

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

Accepted Answer

If you go to the pool, you will want to return.

Answer

If you return to the pool you will enjoy yourself.

Answer

If you enjoy yourself, then you went to the pool.

Answer

No conclusion can be made.

Question 11

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

Accepted Answer

Law of Detachment

Answer

Law of Syllogism

Answer

Law of Contrapositive

Answer

Question 12

Draw a conclusion from the statement.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.

Accepted Answer

Invalid

Answer

Jack skipped school.

Answer

It isn't Monday.

Answer

It's Saturday.

Question 13

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Statement 1: If I study for one hour each day, then I will score well on the exam

Statement 2: I will study from 6pm to 7pm tonite.

Accepted Answer

I will do well on the exam

Answer

I study for several hours each day.

Answer

If I do well on the exam, I studied for hours.

Answer

not possible

Question 14

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...

Accepted Answer

The big test will not be given today.

Answer

Look out for the snowplows while driving to school.

Answer

The roads will be hard to drive on.

Answer

You should call the school to see if school is canceled.

Question 15

Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Accepted Answer

Opposite angles of a rhombus are congruent

Answer

Opposite angles of a quadrilateral are congruent

Answer

Every quadrilateral is a rhombus

Answer

Every parallelogram is a rhombus

Question 16

Use Law of Syllogism to make a conclusion.
If a number is divisible by 10, then it is divisible by 2. If a number is divisible by 2, then it is even.

Accepted Answer

If a number is divisible by 10, then it is even,

Answer

If a number is even, then it is divisible by 10.

Answer

If a number is divisible by 2, then it is even.

Answer

If a number is even, then it is divisible by 2.

Question 17

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.

Accepted Answer

If the perimeter of a square is 20 ft, then the area is 25 ft²

Answer

If the side of a square is 5 ft, then the perimeter is 20 ft.

Answer

If the area of a square is 25 ft², then the side length is 5 ft.

Answer

If the are of a square is 25 ft², then the perimeter is 20 ft.

Question 18

Write the if-then statement that follows from the pair of true statements. If Todd goes to the movies, then Sarah will go to the movies.  If Chris goes to the movies, then Todd will go to the movies.

Accepted Answer

If Chris goes to the movies, then Sarah will go to the movies.

Answer

If Todd goes to the movies, then Chris will go to the movies.

Answer

If Sarah goes to the movies, then Chris will go to the movies.

Answer

If Chris goes to the movies, then Todd will go to the movies.

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