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Reasoning HW Day 4

Total questions: 25

Worksheet time: 1hrs 28mins

Name
Class
Date
1.

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.
If 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.
2.

What can be concluded from the following statements?  (Think Contrapositive)
If Mike rakes leaves, then he bags them .
If Mike bags the leaves then he mows the lawn.

a)
If Mike mows the lawn then he bags the leaves.
b)
If Mike bags the leaves then he rakes.
c)
If Mike does not mow the lawn, then he did not rake the leaves.
d)
If Mike mows the lawn then he bags the leaves.
3.
What conclusion can be drawn from the following statements?
If the stereo is on, then the volume is loud.  
If the volume of the stereo is loud, then the neighbors will complain.
a)
If the neighbors complain, then the stereo will be loud.
b)
If the stereo is on, then the neighbors will complain.
c)
If the stereo is volume is loud, then the stereo is on.
d)
If the stereo is on, then the volume is loud.
4.
What is a conjecture?
a)
A statement believed to be true based on observations.
b)
An example which disproves an hypothesis.
c)
the performance of tricks that are seemingly magical
5.
Find the next term in the sequence:
A, D, G, J, _____
a)
L
b)
M
c)
P
d)
K
6.
Used to prove that a conjecture is false.
a)
Counterexample
b)
Inductive Reasoning
c)
Concluding statement
d)
Conjecture
7.
Which is a counterexample of: The difference of two numbers is less than the greater number.
a)
(5) - (2) = 3
b)

(5) - (4) = 1

c)
(2) - 0 = 2
d)
(3) - (3) = 0
8.
What conclusion can be drawn from the following statements?
If the sun is shining, then it is a beautiful day.  
If it is a beautiful day, then we will have a picnic.
a)
If the sun is shining, then it is a beautiful day.
b)
If it is a beautiful day, then the sun is shining.
c)
If the sun is shining, then we will go on a picnic.
d)
If we go on a picnic, then the sun is shining.
9.
Where would the next red square be?
a)
bottom left
b)
top right
c)
top left
d)
bottom right
10.
What are the next two numbers in this pattern?
12, 17, 22, 27, ___, ___
a)
32, 37
b)
30, 37
c)
30, 33
d)
32, 35
11.
What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73
a)
32, 62
b)
42, 63
c)
43, 63
d)
42, 62
12.
a)
1
b)
15
c)
20
d)
12
13.
What comes next?
a)
The next term will have 16 blocks
b)
The next term will have 15 blocks.
c)
The next term will have 14 blocks.
d)
This is the end of the pattern.
14.

If Lind scores are 50 higher, then she will pass the quiz.

Linda got a score of 55.

What is the possible conclusion?

a)

Linda did not passed the quiz.

b)

Linda passed the quiz.

c)

Linda will get a grade of 95.

d)

Linda will be promoted to another grade.

15.

If Roger gets a job, then he will buy a bike. 

Roger got a job.  

Conclusion: ___________           

                                                             

a)

Roger will not buy a bike.

b)

Roger will buy a bike.

c)

No conclusion

16.

If Mary eats, then she will sleep.

Mary does not eat.

Conclusion: __________

a)

Mary sleeps.

b)

Mary does not sleep.

c)

No conclusion

17.

If it is raining, then the grass gets wet.

It is not raining.

Conclusion: ______________

a)

The grass gets wet.

b)

The grass does not get wet.

c)

No conclusion

18.
Draw a conclusion from the statement.
Given: If you are at least 25 year old, then you can rent a car.
Clay can rent a car.
Conclusion: ?
a)
Clay is at least 25 years old
b)
Clay can rent a car
c)
Clay can go on a road trip
d)
Invalid
19.
(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?
a)
Figure A is a polygon.
b)
Figure A is a circle.
c)
Figure A is a square.
d)
invalid; nothing belongs in line 3
20.

Draw a conclusion from the statement.

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: We can't make any conclusion.

21.

Which of the following is a counterexample to the following conjecture? If x2 = 4x^2\ =\ 4 , then x = 2

a)

x = 4

b)

x = -2

c)

x = 2

d)

x = -4

22.

Which number is a counterexample to the following statement?
For all numbers a, 2a + 7 ≤17\le17  

a)

a = 6

b)

a = 0

c)

a = 5

d)

a = 1

23.
If it is a fraction, then it is a number between zero and one. What is an appropriate counterexample?
a)
2/3
b)
4/5
c)
1/2
d)
3/2
24.
Which is a counterexample of: Any number divisible by 2 is divisible by 4.
a)
15÷2
b)
20÷4
c)
16÷4
d)
10÷2
25.
If it is an angle, then it is acute. What is an appropriate counterexample?
a)
70⁰
b)
45⁰
c)
120⁰
d)
True. There is no counterexample.

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