Free Printable Logical reasoning (diagramatic)

1.

Which is the converse of:
"If a figure is a circle with radius r, then its circumference in 2(pi)r."

a)

If a figure has a circumference of 2(pi)r, then its a circle with radius r.

b)

If a figure doesn't have a circumference, then it's a circle with a radius of r.

c)

If a figure isn't a circle with radius r, then its circumference isn't 2(pi)r

d)

If a figure isn't a circle, then it doesn't have a circumference.

2.

Contrapositive of:
If an integer ends with 0, then it's divisible by 2.

a)

If an integer ends with 2 then it's divisible by 0.

b)

If an integer doesn't end in 0, then it's not divisible by 2.

c)

If an integer isn't divisible by 2, then it's doesn't end in 0.

d)

If an integer is divisible by 2, then it ends with 0.

3.

Inverse of:
If you win the championship game, then you win the league trophy.

a)

If you don't win the championship game, then you don't win the league trophy.

b)

If you win the league trophy, then you win the championship game.

c)

If you don't win the league trophy, then you don't win the championship game.

d)

If you don't play the game, you can't win a trophy.

4.

Which statement is a good definition of a rectangle?

a)

A rectangle is a shape with four sides.

b)

A rectangle is a shape with two pairs of parallel sides.

c)

A rectangle is a quadrilateral with four congruent angles.

d)

A rectangle is a parallelogram with four congruent sides.

5.

Conditional: If a triangle is scalene, then it has no congruent sides.
Which statement shows the conditional written as a true biconditional?

a)

A triangle is scalene if and only if it has no congruent sides.

b)

If a triangle has no congruent sides, then the triangle is scalene.

c)

If a triangle has some congruent sides, then the tringle is not scalene.

d)

A triangle is equilateral if and only if it is not scalene.

6.

Which of the following is a good definition?

a)

grass is green.

b)

A yard is a unit of measure exactly 3 ft long.

c)

Dinosaurs are extinct.

d)

A pound weighs more than an ounce.

7.

Which conclusion can you make?
If a whole number ends in 0, then it is divisible by 10.
If a whole number is divisible by 10, then it is divisible by 5.

a)

If a whole number ends in 10 then it's divisible by 0.

b)

If a whole number ends in 5, then it's divisible by 10.

c)

If a whole number ends in 0, then it's divisible by 5.

d)

No conclusion can be made.

8.

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.

a)

The polygon is a rectangle.

b)

The polygon is a regular quadrilateral.

c)

The polygon has exactly five congruent angles.

d)

The polygon has congruent sides.

9.

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, therefore...

a)

look out for the snowplows while driving to school.

b)

the big test will not be given today.

c)

the roads will be hard to drive on.

d)

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

10.

Which statement is a valid conclusion?
If a student has a temperature of 100 or more, then he/she should stay home from school.
Jake has a temperature of 101 and Suzi has a temperature of 99.

a)

Both Jake and Suzi should stay home.

b)

Both should go see the school nurse.

c)

Jake should stay home, but Suzi should go to school.

d)

Suzi should stay home, but Jake should go to school.

11.

Make a valid conclusion:
If a blub is screaming, then a frot is swimming.
If a frot is swimming, then a greep is flinging.

a)

A blub is flinging.

b)

If a blub is screaming, then a greep is flinging.

c)

A frot is swimming when a blub is screaming.

d)

If a greep is flinging, then a blub is screaming.

12.

Make a valid conclusion:
If it rains then the sky is dark.
If the sky is dark, then crickets will chirp.
Laura is using her umbrella.

a)

The crickets are chirping.

b)

They sky is dark.

c)

Laura is avoiding the rain.

d)

No conclusion can be made.

13.

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

a)

You are at least 25 years old

b)

You can rent a car

c)

You can go on a road trip

d)

Invalid

14.

If the binding of the book is broken, then the student will have to pay for a new one.
Michael has to pay for a new book, so he concludes the binding on his book is broken.
Is he correct?

a)

Yes

b)

No

15.

Determine which one is a statement.

a)

3m x 2m = 6m

b)

A prime number has 2 factors.

c)

χ + γ

d)

Express 2300 in standard form.

e)

χ + 2 = 3

16.

All integers are positive intigers.

a)

no

b)

not

17.

_________ factors of are factors of 6

a)

All

b)

Some

18.

Premise 1 : All rhombuses are parallelgrams.

Premise 2 : __________________________________

Conclusion : A square is a parallelogram.

a)

A square not rhombus

b)

A square is a rhombus

c)

parallelograms is a square

d)

Parallelogram is not a square

19.

which one is a statement

a)

square have 4 side

b)

circle have 3 side

c)

triangle dont have any side

20.

Complete the premise in the following argument.

Premise 1 : If set P is a subset of set Q, then P ∩ Q = P.

Premise 2 : .........................................................................

Premise 3 : Set P is not a subset f set Q.

a)

P ⋃ Q = Q

b)

P ∩ Q = P

c)

P ∩ Q ≠ P

d)

P ⋃ Q ≠ P

21.

state whether the following statement is true or false.

All polygons have five sides.

a)

True

b)

False

22.

complete the following compound statement by writing the word 'or' or 'and' to form a true statement.

4²= 8 [__] 7 x 0 = 0

a)

Or

b)

And

23.

complete the following statement using the quantifier 'all' or 'some', to make it a true statement.

......... integers are even number.

a)

All

b)

Some

24.

choose two implications based on the following statement.

y > 3 if and only if 2y > 6

a)

If y > 3, then 2y > 6

b)

If y < 6 , then 2y > 6

c)

If 2y > 6, then y > 3

d)

If 2y > 6, then y < 6

25.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the converse of this statement?

a)

If a polygon is not a quadrilateral, then it is not a trapezoid.

b)

If a polygon is not a trapezoid, then it is not a quadrilateral.

c)

If a polygon is a trapezoid, then it is a quadrilateral.

d)

A rectangle is also a quadrilateral.

26.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the inverse of this statement?

a)

If the polygon is not a quadrilateral, then it is not a trapezoid.

b)

If the polygon is not a trapezoid, then it is not a quadrilateral.

c)

If the polygon is a trapezoid, then it is a quadrilateral.

d)

A rectangle is also a quadrilateral.

27.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

a)

If a polygon is a trapezoid, then it is a quadrilateral.

b)

If a polygon is not a quadrilateral, then it is not a trapezoid.

c)

If a polygon is not a trapezoid, then it is not a quadrilateral.

d)

A rectangle is also a quadrilateral.

28.

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

a)

Inductive

b)

Deductive

29.

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

a)

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

b)

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

c)

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

d)

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

30.

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

a)

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

b)

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

c)

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

d)

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

31.

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.

a)

I am smart.

b)

I got an A on my test.

c)

My mom will buy me a TV.

d)

I must have cheated.

32.

25 > 43

a)

statement / Pernyataan

b)

non-statement / Bukan Pernyataan

33.

x+y=10

a)

statement / Pernyataan

b)

non-statement / Bukan Pernyataan

34.

11 and 15 is a prime number.

11 dan 15 ialah nombor perdana.

a)

True / Benar

b)

False / Palsu

35.

Look at this series : 53,53,40,40,27,27,.. What number should come next?

a)

12

b)

14

c)

27

d)

53

36.

Which word does NOT belong with the others ?

a)

Inch

b)

Ounce

c)

Centimeters

d)

Yard

37.

Marathon is to race as hibernation is to

a)

Winter

b)

Bear

c)

Dream

d)

Sleep

38.

Find the statement that must be true according to the given information

1. Vincent has a paper route . Each morning, he delivers 37 newspapers to customers in his neighborhood. It takes Vincent 50 minutes to deliver all the papers. If Vincent is sick or has other plans, his friend Thomas, who live on the same street, will sometimes deliver the papers for him.

a)

Vincent and Thomas live in the same neighborhood

b)

It takes Thomas more than 50 minutes to deliver the papers.

c)

It is dark outside when Vincent begins his deliveries

d)

Thomas would like to have his own paper route.

39.

STATEMENT : It is desirable to put the child in school at the age of 5 or so.

ASSUMPTIONS :

1. At that age the child reaches appropriate level of development and is ready to learn.

2. The schools do not admit children after six years of age.

a)

Only assumptions 1 is implicit

b)

Only assumptions 2 is implicit

c)

Either 1 or 2 is implicit

d)

Neither 1 nor 2 is implicit

e)

Both 1 and 2 are implicit

40.

STATEMENTS :

The old order changed yielding place to new.

CONCLUSIONS:

1. Change is the law of nature.

2. Discard old ideas because they are old.

a)

Only conclusion 1 follows

b)

Only conclusion 2 follows

c)

Either 1 or 2 follows

d)

Neither 1 nor 2 follows

e)

Both 1 and 2 follow

41.

CAUSE & EFFECT

STATEMENTS:

1. All the schools in the area had to kept closed for most part of the week.

2. Many parents have withdrawn their children from the local schools.

a)

Statement 1 is the cause and statement 2 is it's effect

b)

Statement 2 is the cause and statement 1 is it's effect

c)

Both the statement 1 and 2 are independent causes

d)

Both the statement 1 and 2 are effects of independent causes

42.

ELFA, GLHA, ILJA,_____,MLNA

a)

OLPA

b)

KLMA

c)

LLMA

d)

KLLA

43.

SCD, TEF, UGH, _____, WKL

a)

CMN

b)

UJI

c)

VIJ

d)

IJT

44.

1.Tanya is older than Eric.

2. Cliff is older than Tanya.

3.Eric is older than Cliff.

If the first two statements are true, the third statement is....

a)

True

b)

False

c)

Uncertain

45.

If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A ?

a)

Brother

b)

Sister

c)

Nephew

d)

Cannot be determined

46.

Arrange the words given below in a meaningful sequence.

1. Key 2. Door 3. Lock 4. Room 5. Switch on

a)

5,1,2,4,3

b)

4,2,1,5,3

c)

1,3,2,4,5

d)

1,2,3,5,4

47.

In the series 2,6,18,54,..... What will be the 8th term ?

a)

4370

b)

4374

c)

7443

d)

7434

48.

A,P,R,X,S and Z are sitting in a row. S and Z are in the centre. A and P are the ends. R is sitting to the left of A. Who is to the right of P ?

a)

A

b)

X

c)

S

d)

Z

49.

Y is in the East of X which is in the North of Z. If P is in the South of Z, then in which direction of Y, is P ?

a)

North

b)

South

c)

South- West

d)

South- East

50.

A man walks 5km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place ?

a)

West

b)

South

c)

North - East

d)

South-West

51.

QUESTION :

In which year was Rahul born ?

STATEMENTS:

1. Rahul at present is 25 years younger to his mother.

2. Rahul's brother,who was born in 1964,is 35 years younger to his mother.

a)

1 alone is sufficient while 2 alone is not sufficient

b)

2 alone is sufficient while 1 alone is not sufficient

c)

Either 1 or 2 is sufficient

d)

Neither 1 nor 2 is sufficient

e)

Both 1and 2 are sufficient

52.

Introducing a boy, a girl said , " He is the son of the daughter of the father of my Uncle."How is the boy related to the girl ?

a)

Brother

b)

Nephew

c)

Uncle

d)

Son- in- law

53.

0,2,8,14,?,34. Find the missing term.

a)

20

b)

23

c)

24

d)

25

54.

Which word does NOT belong with the others?

a)

Heading

b)

Body

c)

Letter

d)

Closing

55.

Determine the antecedent and consequent of the statement:
"If the perimeter of a rectangle A is 2(x+y), then the area of rectangle is xy."

a)

Antecedent: The area of rectangle A is xy
Consequent: Perimeter of rectangle A is 2(x+y)

b)

Antecedent: The area of rectangle A is xy
Consequent: Perimeter of rectangle A is 2x+y

c)

Antecedent: Perimeter of rectangle A is 2x+y
Consequent: The area of rectangle A is xy

d)

Antecedent: Perimeter of rectangle A is 2(x+y)
Consequent: The area of rectangle A is xy

56.

Write an appropriate implication based on the following pairs of implications:

a) If x is a multiple of 10, then x is a multiple of 5.

b) if x is a multiple of 5, then x is a multiple of 10.

(a)

57.

$"If\ w>20,\ then\ w>30."$

Find the contrapositive for the statement and decide if it is a true or false statement.

a)

$if\ w\le20,\ then\ w\le30.$ True.

b)

$if\ w>30,\ then\ w>20.$ False.

c)

$if\ w\ge20,\ then\ w\ge30.$ True.

d)

$if\ w\le30,\ then\ w\le20.$ False.

58.

$premise\ 1:\ All\ factors\ of\ 4\ are\ factors\ of\ 8$ $premise\ 2:\ 2\ is\ a\ factor\ of\ 4$
$conclusion:$ (a)

Complete the argument to form valid and sound deductive argument.

59.

$premise\ 1:\ All\ factors\ of\ 4\ are\ factors\ of\ 8$ $premise\ 2:\ 2\ is\ a\ factor\ of\ 4$
$conclusion:$ (a)

Complete the argument to form valid and sound deductive argument.

60.

Given the surface are of a cone $=\pi r\left(r+s\right),$ make a conclusion by deduction for the surface area of the five similar cones such that r=7cm and s=13cm.

a)

$Surface\ area\ of\ five\ cones\ is\ 700\pi$

b)

$Surface\ area\ of\ five\ cones\ is\ 140\pi$

c)

$Surface\ area\ of\ five\ cones\ is\ 540\pi$

d)

$Surface\ area\ of\ five\ cones\ is\ 1080\pi$

61.

$premise\ 1:\ Mas\ got\ A+\ for\ Mathematic$ $premise\ 2:\ Yazmeen\ got\ A+\ for\ Mathematic$ $premise\ 3:\ Amna\ got\ A+\ for\ Mathematic$ $conclusion:\ All\ students\ in\ 4E\ got\ A+\ for\ Mathematic\$ Determine whether the given argument are strong or weak, and cogent or not cogent.

a)

Strong and cogent

b)

Strong and not cogent

c)

Weak and cogent

d)

Weak and not cogent

62.

Determine whether the argument are inductive or deductive arguments.
"All the students from class 4E perform on Teachers' Day. Wahida is a pupil from class 4E. Then Wahida performs on Teachers' Day."

a)

Inductive argument

b)

Deductive argument

63.

Determine whether the argument is inductive or deductive arguments.

The sum of 1 and 3 is an even number.

The sum of 3 and 5 is an even number.

The sum of 5 and 7 is an even number.

The sum of 7 and 9 is an even number.

In conclusion, the sum of two odd number is an even number.

a)

Inductive argument

b)

Deductive argument

64.

Determine which type of argument have the following criteria.
Premise 1: if p, then 1.
Premise 2: Not q is true.
Conclusion: Not p is true.

a)

Argument Form 1

b)

Argument Form 2

c)

Argument Form 3

d)

Argument Form 4

65.

Determine whether the following argument is valid or not valid, or sound or not sound.

Premise 1: All rhombus have perpendicular diagonals.

Premise 2: PQRS has perpendicular diagonals.

Conclusion: PQRS is a rhombus

a)

Valid and sound

b)

Valid and not sound

c)

Not valid and sound

d)

Not valid and not sound

66.

Which is the converse of:
"If a figure is a circle with radius r, then its circumference in 2(pi)r."

a)

If a figure has a circumference of 2(pi)r, then its a circle with radius r.

b)

If a figure doesn't have a circumference, then it's a circle with a radius of r.

c)

If a figure isn't a circle with radius r, then its circumference isn't 2(pi)r

d)

If a figure isn't a circle, then it doesn't have a circumference.

67.

Contrapositive of:
If an integer ends with 0, then it's divisible by 2.

a)

If an integer ends with 2 then it's divisible by 0.

b)

If an integer doesn't end in 0, then it's not divisible by 2.

c)

If an integer isn't divisible by 2, then it's doesn't end in 0.

d)

If an integer is divisible by 2, then it ends with 0.

68.

Determine which one is a statement.

a)

3m x 2m = 6m

b)

A prime number has 2 factors.

c)

χ + γ

d)

Express 2300 in standard form.

e)

χ + 2 = 3

69.

(a)

70.

a)

a

b)

b

c)

c

d)

d

71.

In this room two people go in and three come out, what am I ?

(a)

72.

What comes once in a minute, twice in a moment and never in a thousand years

(a)

73.

(a)

74.

a)

1

b)

2

c)

3

d)

4

75.

a)

a

b)

b

c)

c

d)

d

76.

a)

a

b)

b

c)

c

d)

d

77.

a)

1

b)

2

c)

3

78.

There was a plane crash, every single person died then who survived

(a)

79.

a)

a

b)

b

c)

c

d)

d

80.

(a)

81.

a)

b)

c)

d)

82.

a)

b)

c)

d)

83.

a)

28

b)

32

c)

18

d)

54

84.

a)

15

b)

11

c)

8

d)

9

85.

a)

b

b)

c

c)

a

86.

a)

72

b)

24

c)

48

d)

36

87.

a)

2

b)

6

c)

10

d)

8

88.

(a)

89.

Match the following:

a)

3, 1, 2

b)

2, 1, 3

c)

1, 2, 3

d)

3, 2, 1

90.

Name the shapes.

(a)

91.

Where would the next red square be?

a)

bottom left

b)

top right

c)

top left

d)

bottom right

92.

How many cubes would be in the 10th figure?

a)

18

b)

16

c)

17

d)

41

93.

How many squares are in Figure 4?

a)

10

b)

11

c)

12

d)

13

e)

14

94.

What is the rule for this pattern?

32,36,40,44

a)

add 4

b)

multiply 2

c)

subtract 4

d)

divide by 2

95.

Using the statements:

If it is Friday, then I will get paid.

It is Friday.

What is the conclusion?

a)

It is not Friday

b)

It is Friday

c)

I will not get paid

d)

I will get paid

96.

Using deductive reasoning, 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...

a)

Look out for the snowplows while driving to school.

b)

The big test will not be given today.

c)

The roads will be hard to drive on.

d)

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

97.

Using deductive reasoning, 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...

a)

Look out for the snowplows while driving to school.

b)

The big test will not be given today.

c)

The roads will be hard to drive on.

d)

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

98.

All chickens that we have seen have been brown.

Using inductive reasoning what can we conclude?

a)

All chickens are brown

b)

All birds are chickens

c)

There are different breeds of chickens here

d)

We cannot conclude anything.

99.

Identify the hypothesis and conclusion of the conditional statement:

If you give me twenty dollars, then I will be your best friend.

a)

Hypothesis: I will be your best friend

Conclusion: you give me twenty dollars

b)

Hypothesis: you give me twenty dollars

Conclusion: I will be your best friend

c)

Hypothesis: if you have to pay for friends

Conclusion: then you probably should reevaluate your life

d)

Hypothesis: you will not have to pay twenty dollars

Conclusion: if you have lots of friends

100.

If something is a vehicle, then it is a Ford. What is an appropriate counterexample?

a)

Ford Mustang

b)

Dodge Charger

c)

Ford F150

d)

Ford C-Max

101.

When taking the converse of a conditional statement, we ___________ the hypothesis and conclusion.

a)

negate

b)

switch

c)

highlight

d)

switch and negate

102.

Which is the correct if-then statement for: "you will be late to school if you miss the bus."

a)

If you are late to school, then you will miss the bus.

b)

If you miss the bus, then you will be late to school

c)

If you sleep late, then you don't have to go to school.

d)

If you miss the bus, then you'll have to walk and be late.

103.

Original: If Emily is not late to class, then she will not be marked tardy.

What is this? If Emily is late to class, then she will be marked tardy.

a)

Converse

b)

Inverse

c)

Contrapositive

d)

Negation

104.

All of the players on the roster are over 6 feet tall. Who is a counterexample of this false statement?

(a)

105.

The diagram shows the sports played by 80 students.

Why is the statement all student either play Football, Hockey, or Rugby false?

a)

Because there is 1 student outside the Football, Hockey, and Rugby circles.

b)

Because we are triple counting the 31 students in the intersection of the Football, Hockey, and Rugby circles.

c)

Because the number of students only adds up to 79 students total.

d)

Because there are only three sports offered at this particular school.

106.

The diagram shows the sports played by 80 students.

Why is the statement all student either play Football, Hockey, or Rugby false?

a)

Because there is 1 student outside the Football, Hockey, and Rugby circles.

b)

Because we are triple counting the 31 students in the intersection of the Football, Hockey, and Rugby circles.

c)

Because the number of students only adds up to 79 students total.

d)

Because there are only three sports offered at this particular school.

107.

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

a)

If you return to the pool you will enjoy yourself.

b)

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

c)

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

d)

No conclusion can be made.

108.

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.

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.

Logical reasoning (diagramatic)

Total questions: 108

Worksheet time: 3hrs 43mins

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