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Inductive Reasoning, Conditionals (Converses, Bi-Conditionals), Deductive Reasoning, and Algebraic Proofs

Total questions: 40

Worksheet time: 29mins

Name
Class
Date
1.

Inductive reasoning is reasoning based on the following:

a)

patterns and observations

b)

given facts

c)

how to solve an equation

d)

given statements

2.

Deductive reasoning is reasoning based on the following:

a)

patterns and observations

b)

given facts and statements

c)

how to solve an equation

d)

prior knowledge

3.

A ________ is a conclusion reached using inductive reasoning.

a)

counterexample

b)

conjecture

c)

hypothesis

d)

conditional

4.

To prove a conjecture is false you must provide a __________.

a)

conjecture

b)

hypothesis

c)

counterexample

d)

converse

5.

A ____________ is a statement that can be written in if-then form.

a)

converse

b)

conclusion

c)

bi-conditional

d)

conditional

6.

The _______________ of a conditional is the phrase immediately following the word if.

a)

conclusion

b)

converse

c)

switch

d)

hypothesis

7.

The _______________ of a conditional is the phrase immediately following the word then.

a)

conclusion

b)

converse

c)

switch

d)

hypothesis

8.

The converse of a conditional is formed by ____________ the hypothesis and conclusion.

a)

deleting

b)

switching

c)

copying

d)

negating

9.

A ____________ is the combination of a conditional and its converse.

a)

bi-conditional

b)

statement

c)

conjecture

d)

counterexample

10.

To use the Law of Detachment, the given information must contain ____________ conditional (if-then) statements.

a)

0

b)

1

c)

2

d)

4

11.

To use the Law of Syllogism, the given information must contain ____________ conditional (if-then) statements.

a)

0

b)

1

c)

2

d)

4

12.
Which of the following conjectures is false?
a)
The product of two even numbers is even.
b)
The sum of two even numbers is even.
c)
The product of two odd numbers is odd.
d)
The sum of two odd numbers is odd.
13.
Find the next item in the pattern:
-3, 6, -12, 24, ...
a)
36
b)
-36
c)
48
d)
-48
14.

What is the hypothesis of the following statement:


"If Johnny is late to school, then his mom will have to drive him."

a)

His mom will have to drive him

b)

late to school

c)

Johnny is late to school

d)

Then his mom will have to drive him

15.

Given the conditional;

"If Jose eats fish, then he has an allergic reaction"

Which of the following is the converse?

a)

None of these

b)

If Jose doesn't have an allergic reaction, then he didn't eat fish.

c)

If Jose doesn't eat fish, then he doesn't have an allergic reaction.

d)

If Jose has an allergic reaction, then he ate fish.

16.

Given the conditional;

"If Destiny goes to work tonight, then she will make money"

What is the conclusion?

a)

Destiny goes to work tonight

b)

Destiny doesn't go to work

c)

She will make money

d)

then she will make money

17.
Write the converse:      
If a figure has four sides, then it is a square.
a)
If a figure is not a square, then it does not have four sides.
b)
If a figure does not have four sides, then it is not a square.
c)
If a figure is a square, then it has four sides.
18.

Which of these is a counterexample to the following statement?

All farm animals have four legs.

a)

Cows

b)

Penguins

c)

Elephants

d)

Chickens

19.

Which of these is a counterexample to the following statement?

All vegetables are green.

a)

Banana

b)

Pumpkins

c)

Green Beans

d)

Grass

20.
  Rewrite the following statement as a      biconditional: "Supplementary angles add up to 180"
a)
If two angles add up to 180o then they are supplementary.
b)
You can't it is conditional.
c)
Two angles are supplementary if and only if the sum of the measure of the two angles is 180o.
d)
If two angles sum does not equal 180o then they are not supplementary.
21.

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

a)

if

b)

then

c)

if and only if

d)

always

22.

What counterexample makes the following biconditional false?


"It is Halloween if and only if it is October 31."

a)

This is a true biconditional, so it has no counterexamples.

b)

It is not October 31.

c)

I don't celebrate Halloween.

d)

It is October 30.

23.

Identify the symbolic notation: p---->q

a)

conditional

b)

converse

c)

bi-conditional

24.

Identify the symbolic notation: p<---->q

a)

conditional

b)

converse

c)

bi-conditional

25.

Identify the symbolic notation: q---->p

a)

conditional

b)

converse

c)

bi-conditional

26.
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.
a)
Invalid
b)
Valid
c)
Sammy is a Great Dane
d)
Sammy is really a cat.
27.
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
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
28.
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
a)
 I study for 1 hour each day.
b)
I do not study for 1 hour each day
c)
If I do well on the exam, I studied for 1 hour each day.
d)
not possible
29.

If this wind keeps up, then we will lose some trees. We lose some trees.


Andy concludes that the wind keeps up.


Is he correct?

a)

Yes, by the Law of Detachment.

b)

No; the Law of Detachment doesn't work here because we weren't told the hypothesis was true.

30.
p → q
p
∴ q
Which law of logic?
a)
Converse Error
b)
Inverse Error
c)
Law of Contrapositive
d)
Law of Detachment
31.
p → q
q → r
∴ p → r
Which law of logic?
a)
Converse Error
b)
Inverse Error
c)
Law of Detachment
d)
Law of Syllogism
32.
For any numbers a, b, and c, if a = b and b = c, then a = c.
a)
Transitive Property         
b)
Symmetric Property
c)
Reflexive Property
d)
Substitution Property
33.
For any numbers a and b, if a = b, then b = a.
a)
Transitive Property         
b)
Reflexive Property 
c)
Symmetric Property   
d)
Substitution Property
34.
If 3x + y = 14 and y = 9, then 3x + 9 = 14.
a)
Reflexive Property of Equality
b)
Symmetric Property of Equality
c)
Transitive Property of Equality
d)
Substitution Property of Equality
35.
3(w + 4) = 3w + 12 is an example of...
a)
Inverse Property
b)
Distributive Property
c)
Multiplicative Inverse
d)
Associative Property
36.
What is reason 1?
a)
Symmetric Property of Equality
b)
Given
c)
Prove
d)
Subtraction Property of Equality
37.
What is reason 2?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
38.
What is reason 3?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
39.
What is step 4
a)
Substitution property (simplify)
b)
Addition property of equality
c)
Subtraction property of equality
40.
What is step 6
a)
Subtraction property of equality
b)
Addition property of equality
c)
Division property of equality