Quiz about Law of Detachment and Syllogism

Question 1

If a student wants to go to university, then the student must study hard and write a good application. Zach wants to go to Caltech.

Accepted Answer

Zach must study hard and write a good application.

Answer

No Conclusion can be made.

Answer

Zach will not study but will write a good application.

Answer

Zach got accepted to Caltech.

Question 2

If two lines do not intersect then they are coplanar and parallel, or skew. Lines AB and CD do not intersect.

Accepted Answer

Lines AB and CD are parallel and coplanar or they are skew.

Answer

Lines AB and CD are parallel and not coplanar.

Answer

Lines AB and CD are skew.

Answer

No Conclusion can be made.

Question 3

If there is lightening, then it is not safe to be out in the open. Mary sees lightening from her home.

Accepted Answer

It is not safe for Marty to be out in the open.

Answer

It is not safe for the lightening

Answer

No conclusion can be made.

Answer

There is lightening.

Question 4

If we see John on Monday, then we can ask him over for lunch. We see John on Monday.

Accepted Answer

We asked John to have lunch with us.

Answer

John may eat with us.

Answer

John saw us on Monday

Answer

No conclusion can be made since the hypothesis did not occur.

Question 5

If two planes intersect, then their intersection is a line. If two planes are not parallel, then they intersect.

Accepted Answer

If two planes are not parallel, then their intersection is a iine.

Answer

No Conclusion can be made.

Answer

If two planes intersect they are not parallel.

Answer

If two planes are parallel, then they do not intersect.

Question 6

If it rains on Tuesday we will not go to the park on Tuesday.

If we do not go to the park on Tuesday we will go on Wednesday.

Accepted Answer

If it rains on Tuesday, we will go Wednesday.

Answer

If we go to the park on Wednesday, then it rained on Tuesday.

Answer

No conclusion can be made.

Answer

If we go to the park on Tuesday, then it rained on Tuesday.

Question 7

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 8

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 9

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

Accepted Answer

I will get paid

Answer

It is not Friday

Answer

It is Friday

Answer

I will not get paid

Question 10

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 11

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 12

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

Accepted Answer

Therefore, the polygon has exactly five congruent angles.

Answer

Therefore, the polygon is a rectangle.

Answer

Therefore, the polygon is a regular quadrilateral.

Answer

Therefore, the polygon has congruent sides.

Question 13

(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?

Accepted Answer

Law of Detachment

Answer

Law of Syllogism

Answer

Law of Contrapositive

Answer

invalid

Question 14

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3) ???????
What belongs in line 3?

Accepted Answer

invalid; nothing belongs in line 3

Answer

Figure A is a polygon.

Answer

Figure A is a circle.

Answer

Figure A is a square.

Question 15

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 16

Using the Law of Detachment, what can you conclude?
If x has a value of 4, then 2x has a value of 8.
The value of x is 4.

Accepted Answer

2x has a value of 8

Answer

x = 4

Answer

no conclusion can be made

Answer

2x does not have a value of 8

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 the sun is shining, then it is a beautiful day.  If it is a beautiful day, then we will have a picnic.

Accepted Answer

If the sun is shining, then we will go on a picnic.

Answer

If the sun is shining, then it is a beautiful day.

Answer

If it is a beautiful day, then the sun is shining.

Answer

If we go on a picnic, then the sun is shining.

Question 19

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.

Question 20

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

Accepted Answer

If Tom goes fishing then he catches a fish.

Answer

If Tom brings his pole then he goes fishing

Answer

If Tom catches a fish then he brought his pole.

Answer

If Tom brings his pole then he catches a fish.

Question 21

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.
If Steve sits on the bench, then Ronald starts at center.

Accepted Answer

If Jason plays basketball then Ronald starts at center.

Answer

If Steve sits on the bench then Jason plays basketball.

Answer

If Ronald starts at center then Jason plays basketball.

Answer

If Steve sits the bench then Ronald does not start at center.

Question 22

For the inverse we _________ the hypothesis and conclusion

Accepted Answer

negate

Answer

switch

Answer

switch and negate

Question 23

For the contrapositive we _________ the hypothesis and conclusion

Accepted Answer

switch and negate

Answer

switch

Answer

negate

Question 24

What does this mean?

Accepted Answer

Inverse Statement

Answer

Conditional Statement

Answer

Converse Statement

Answer

Contrapositive Statement

Question 25

What is this?

Accepted Answer

Conditional Statement

Answer

Inverse

Answer

Converse

Answer

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

Question 26

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

Accepted Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 27

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

Accepted Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 28

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

Accepted Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 29

What is the hypothesis of the following statement: "If Johnny is late to school, then his mom will have to drive him."

Accepted Answer

Johnny is late to school

Answer

His mom will have to drive him

Answer

If Johnny is late to school

Answer

Then his mom will have to drive him

Question 30

Given: If I get an A on my test then my mom will buy me a TV.
I got a 94 on my test.
what conclusion can be made.

Accepted Answer

My mom will buy me a TV.

Answer

I am smart.

Answer

I got an A on my test.

Answer

I must have cheated.

Question 31

Write a counterexample for the following conditional:
If an electronic device has a screen then it is a television.

Accepted Answer

cellular phone

Answer

television

Answer

computer mouse

Answer

keyboard

Question 32

If the inverse statement is true then you can conclude that the converse statement is true.

Accepted Answer

False

Answer

True

Question 33

If the condition statement is true then you can conclude that the contrapositive statement is true.

Accepted Answer

true

Answer

false

Question 34

If the inverse statement is false then you can conclude that the converse statement is false.

Accepted Answer

true

Answer

false

Question 35

How many senior boys play football and wrestle?

Accepted Answer

9

Answer

12

Answer

18

Answer

39

Question 36

How many senior boys play football but do not wrestle?

Accepted Answer

18

Answer

9

Answer

12

Answer

104

Question 37

How many senior boys play football or wrestle?

Accepted Answer

39

Answer

9

Answer

21

Answer

30

Question 38

How many students took the survey?

Accepted Answer

53

Answer

32

Answer

47

Answer

56

Question 39

How many students do not snowboard?

Accepted Answer

28

Answer

21

Answer

22

Answer

29

Question 40

How many students do not ski or ice skate?

Accepted Answer

16

Answer

10

Answer

22

Answer

28

Question 41

What does the shaded portion of the Venn diagram represent?

Accepted Answer

p

Answer

Not p

Answer

p and q

Answer

p or q

Question 42

What does the shaded portion of the Venn diagram represent?

Accepted Answer

p and q

Answer

Not p

Answer

p or q

Answer

Not q

Question 43

What does the shaded portion of the Venn diagram represent?

Accepted Answer

Only Art

Answer

Band and Art

Answer

Band or Art

Answer

Neither

Question 44

What does the shaded region of the Venn diagram represent?

Accepted Answer

Only P and S

Answer

P or S

Answer

Only P or S

Answer

P and S

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