Arguments-Inductive Deductive

Multiple Choice

The moon was full 4 weeks ago, so it should be full again tonight.

• Inductive argument

• Deductive Argument

Multiple Choice

Deductive arguments...

• can be said to be valid or invalid, or sound/unsound

• can be said to be weak or strong.

Multiple Choice

What reasoning makes predictions based on patterns and observations?

• Inductive

• Deductive

Multiple Choice

Which type of argument claims that the truth of the premises guarantees the truth of the conclusion?

• Deductive argument
• Non-deductive argument
• Abductive argument
• Analogical argument

Multiple Choice

Obtuse angles are greater than 90 degrees.  This angle is 110 degrees, so it is obtuse. 

• Deductive
• Inductive

Multiple Choice

Snakes are reptiles and reptiles are cold blooded; therefore, snakes are cold blooded. 

• Deductive
• Inductive 

Explanation Slide...

Deductive arguments are structured so that if the premises are true, the conclusion must also be true.

Multiple Choice

All observed houses on South Street have roofs that are falling apart.  Sherry lives on South Street.  Her roof is falling apart. 

• Deductive
• Inductive

Multiple Choice

What does deductive reasoning use to form its arguments?

• patterns

• specific cases

• observed examples

• facts, definitions, accepted properties, and laws of logic

Multiple Choice

IF 3...6...9...12...
AND 24...27...30...?
THEN the next term is going to be 33

• Inductive
• Deductive

Multiple Choice

What term refers to statements or propositions that provide support for the conclusion of an argument?

• Conclusions
• Proofs
• Premises
• Inferences

Multiple Choice

IF All even numbers are divisible by 2
AND 28 is even
THEN 28 is divisible by 2

• Inductive
• Deductive

Multiple Choice

A sound argument is a valid argument with true premises

• True

• False

Multiple Choice

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.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Explanation Slide...

Premises are the statements or propositions that are used as evidence or reasons to support a conclusion.

Multiple Choice

The type of reasoning where a person makes  conclusions based on observations and patterns is called...

• Inductive reasoning
• Deductive reasoning
• Conjecture
• Experiments

Multiple Choice

Determine the type of reasoning:

I got up at six o'clock for the past week. I will get up at 6 tomorrow.

• Inductive

• Deductive

• Neither

Multiple Choice

What is a conjecture?

• A statement believed to be true based on observations.
• An example which disproves an hypothesis.
• the performance of tricks that are seemingly magical

Multiple Choice

What is the main characteristic of a non-deductive argument?

• The premises guarantee the conclusion.
• The premises contradict the conclusion.
• The premises offer probable support for the conclusion.
• The premises are necessarily false.

Multiple Choice

Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________

• even
• odd
• zero
• positive

Multiple Choice

I hear you’ve been diagnosed with Lyme disease. You should go to the doctor and get some antibiotics for it. When Saheed was given antibiotics for his Lyme disease, his symptoms cleared up in a few weeks. The same happened with Arquelina when she had it.

• Inductive Argument

• Deductive Argument

Multiple Choice

Find the next term in the sequence:
A, D, G, J, _____

• L
• M
• P
• K

Explanation Slide...

Non-deductive arguments provide support that is probable rather than certain, meaning the conclusion is likely but not guaranteed.

Multiple Choice

How many cubes would be in the 10th figure?

• 18
• 16
• 17
• 41

Multiple Choice

Determine the type of reasoning:

Miguel has 20 pencils. He gives half of them to Ivy. Miguel has 10 pencils.

• Inductive

• Deductive

• Neither

Multiple Choice

Used to prove that a conjecture is false.

• Counterexample
• Inductive Reasoning
• Concluding statement
• Conjecture

Multiple Choice

In logical reasoning, what is a conclusion?

• An unrelated proposition
• A type of premise
• A deductive argument
• A statement that follows from premises

Multiple Choice

Which is a counterexample of: The difference of two numbers is less than the greater number.

• (5) - (2) = 3
• (-5) - (4) = -9
• (2) - 0 = 2
• (3) - (3) = 0

Multiple Choice

Inductive arguments...

• Are outside-in: start general and then get specific

• Are inside-out: start specific and then get general

Multiple Choice

Which number is a counterexample to the following statement? : 
All numbers that are divisible by 2 are divisible by 4

• 0
• 12
• 28
• 42

Explanation Slide...

The conclusion is the statement that the premises are intended to support or prove.

Multiple Choice

What does deductive reasoning use to form its arguments?

• patterns

• specific cases

• observed examples

• facts, definitions, accepted properties, and laws of logic

Multiple Choice

Determine the type of reasoning:

In the sequence, 1, 2, 4, 7, 11, 16, the next most probable number is 22.

• Inductive

• Deductive

• Neither

Multiple Choice

Which of the following is true of a deductive argument?

• The conclusion is always probably true.
• If the argument is valid and the premises are true, the conclusion must be true.
• The conclusion is based on empirical evidence.
• The premises and the conclusion are both propositions.

Explanation Slide...

In a valid deductive argument, true premises ensure that the conclusion is also true, which is why such arguments are considered logically certain.

Multiple Choice

Determine the type of reasoning:

Gas prices have gone down for the past few days. The price of gas will go down tomorrow.

• Inductive

• Deductive

• Neither

Multiple Choice

Which term refers to the process of demonstrating the truth of a conclusion through logical reasoning?

• Deductive argument
• Proof
• Premise
• Proposition

Multiple Choice

Inductive arguments...

• can be strong or weak

• can be valid or invalid

Explanation Slide...

A proof is a logical process that demonstrates the truth of a conclusion by following a series of valid inferences from true premises.

Multiple Choice

Determine the type of reasoning:

The World Cup is held every four years. The last time it was held was in 2018. The next World Cup will be in 2022.

• Inductive

• Deductive

• Neither

Multiple Choice

If an argument's premises are true and the argument is valid, what can we say about the conclusion?

• It is sound.
• It is necessarily true.
• It is proof.
• It is cogent.

Multiple Choice

Jae is a student at City College. No students at City College live on campus. Therefore, Jae does not live on campus.

• Inductive Argument

• Deductive Argument

Explanation Slide...

In a valid deductive argument with true premises, the conclusion must also be true; this is a defining feature of such arguments.

Multiple Choice

Determine the type of reasoning:

Every even number is divisible by 2. 1986 is an even number, therefore it is divisible by two.

• Inductive

• Deductive

• Neither

Multiple Choice

What is the difference between a proposition and a premise?

• A proposition is a statement, while a premise provides support.
• A premise is always true, but a proposition is not.
• A proposition is the conclusion, and a premise is an assumption.
• They are the same in deductive arguments.

Explanation Slide...

Deductive reasoning can be valid or invalid

Explanation Slide...

A proposition is any declarative statement, while a premise is a proposition that is used as evidence in an argument.

Multiple Choice

Determine the type of reasoning:

Every president of the United States has been male. The next two presidents will be male.

• Inductive

• Deductive

• Neither

Multiple Choice

Which type of argument is most likely to be used in mathematical proofs?

• Non-deductive argument
• Deductive argument
• Inductive argument
• Analogical argument

Explanation Slide...

Mathematical proofs rely on deductive reasoning, where the truth of the premises ensures the truth of the conclusion.

Fill in the Blank

Determine the next number in the sequence:

1, 1, 2, 3, 5, 8, _

Multiple Choice

What does it mean if an argument is described as "sound"?

• It is an inductive argument with a strong conclusion.
• It has premises that are true, but the conclusion is false.
• It is a non-deductive argument with probable support.
• It is a deductive argument with true premises and a true conclusion.

Multiple Choice

Inductive reasoning involves using patterns to come up with broader generalizations

• True

• False

Explanation Slide...

A sound argument is a valid deductive argument with all true premises, meaning the conclusion must also be true.

Multiple Choice

Obtuse angles are greater than 90 degrees.  This angle is 110 degrees, so it is obtuse. 

• Deductive
• Inductive

Multiple Choice

What is a valid argument?

• An argument where the premises, if true, guarantee the truth of the conclusion
• An argument where the premises are true, but the conclusion is false
• An argument where the premises do not support the conclusion
• An argument with a weak conclusion

Multiple Choice

I think we can trust James to keep his promise. He’s never broken a promise he’s made to me in the past.

• Inductive Argument

• Deductive Argument

Explanation Slide...

A valid argument is one where, if the premises are true, the conclusion must be true as well.

Multiple Choice

Snakes are reptiles and reptiles are cold blooded; therefore, snakes are cold blooded. 

• Deductive
• Inductive 

Multiple Choice

What is an invalid argument?

• An argument where the premises guarantee the conclusion
• An argument where the conclusion is always true
• An argument where the premises do not guarantee the conclusion
• An argument that is sound

Multiple Choice

Inductive arguments have premises that can offer a likely conclusion

• True

• False

Explanation Slide...

An invalid argument is one where the premises do not logically guarantee the conclusion, even if the premises are true.

Multiple Choice

Complete the conjecture.  Think of examples to help.
The product of any two odd numbers is _____________

• even
• odd
• zero
• positive

Multiple Choice

What is a sound argument?

• An argument that is valid and has all true premises
• An argument that is valid but has false premises
• An argument that is invalid but has true premises
• An argument that is invalid with false premises

Explanation Slide...

A sound argument is both valid and has all true premises, ensuring that the conclusion is true.

Multiple Choice

Find the next term in the sequence:
A, D, G, J, _____

• L
• M
• P
• K

Multiple Choice

What is an unsound argument?

• An argument that is valid and has true premises
• An argument that is valid but has at least one false premise
• An argument that is invalid and has all true premises
• An argument that is invalid but has a true conclusion

Multiple Choice

All bachelors are unmarried men. John is an unmarried man. Therefore, John is a bachelor.

• This is an inductive argument.

• This is a deductive argument.

Explanation Slide...

An unsound argument is a valid argument that has at least one false premise, or an invalid argument regardless of the premises.

Multiple Choice

The 11th figure will be a...

• triangle

• square

• rhombus

• circle

Multiple Choice

What is a cogent argument?

• A strong inductive argument with true premises
• A weak deductive argument with true premises
• A strong deductive argument with false premises
• A valid deductive argument with false premises

Multiple Choice

Young people are more technology literate these days. So you are better off asking your little cousin Adrienne for help with your phone than you are her dad.

• Inductive Argument

• Deductive Argument

Explanation Slide...

A cogent argument is a strong inductive argument with true premises, making the conclusion likely to be true.

Multiple Choice

37, 34, 31, 28
Which number should come next in the pattern?

• 24
• 23
• 25
• 27

Explanation Slide...

This example illustrates deductive reasoning by starting with a general premise, ‘all bachelors are unmarried men,’ and then shrinking the statement to apply to the particular or specific instance.In this case: John is a man, and he is not married; therefore, John is a bachelor. The conclusion is indisputable, unlike in inductive reasoning, where the conclusions are just educated guesses.

Multiple Choice

For five years in a row, I have seen bears in the woods in June but not May. This year, I expect to wait until June to see a bear in the woods.

• This is a valid deductive argument.

• This is a weak inductive argument.

• This is a strong inductive argument.

• This is an invalid deductive argument.

Multiple Choice

While many countries in the European Union have adopted the Euro, the only Scandinavian country that has adopted it is Finland. Therefore, Sweden does not use the Euro as its currency.

• Inductive Argument

• Deductive Argument

Explanation Slide...

In this example, a person who lives near the woods has identified a seasonal trend that allows them to generalize and predict future patterns. This sort of seasonal prediction has been around for millennia. Agriculturalists use seasonal trends to reason about when to plant their seeds. This doesn’t mean every year will be perfect (to this day, some seasons are terrible for crop yield).

Multiple Choice

Anyone born in late August to late September is a Virgo. Ashley was born on September 4th. Therefore, Ashley is a Virgo.

• This is an inductive argument.

• This is a deductive argument.

Multiple Choice

We’re willing to put down our dogs and cats when they are old and sick. Why shouldn’t we do the same with our elderly?

• Inductive Argument

• Deductive Argument

Explanation Slide...

While deductive logic goes from the top-down, based on the set of premises given in this example it’s clear that we could induce (or build-up,) to the correct conclusion as well.Bottom-up reasoning, or arriving at a broad conclusion based on specific premises is known as inductive reasoning, and is in contrast to deductive reasoning.

Multiple Choice

All my siblings are left-handed, and we are all talented artists. People that are left-handed are more creative and artistically inclined than those that are right-handed.

• This is a weak inductive argument.

• This is a weak deductive argument.

• This is a sound inductive argument.

• This is an invalid deductive argument.

Multiple Choice

Mike weighed 210 pounds before going on a diet three months ago. He has lost 17 pounds so far on the diet. Therefore, he now weighs less than 200 pounds.

• Inductive Argument

• Deductive Argument

Explanation Slide...

It could seem reasonable for this person to assume (based on the evidence that they are exposed to) that left-handed people are naturally more creative and artistic than their right-handed counterparts. Despite appearances, it is not proven that left-handed people are in fact more artistic than right-handed people.The misstep in logic occurs from making the move from the specific to the general without having sufficient evidence to substantiate the claim as a generally applicable rule.

Multiple Choice

While shopping for groceries, I was in the produce section checking for ripe avocados. I picked up one avocado and it was not ripe enough to eat. I picked up another and it was also underripe. There must not be any ripe avocados at this grocery store.

• This is a sound deductive argument.

• This is a sound inductive argument.

• This is a weak inductive argument.

Explanation Slide...

Picking up a few avocados and determining that they are not ripe enough to eat does not necessarily indicate the remaining avocados in the bin will be underripe. This abrogates logic and demonstrates the error in inductive reasoning.

Multiple Choice

Ray lives in Canada, and he knows it gets extremely cold during the winter. Since it is approaching winter, Ray decided to buy a parka to get him through the winter seasons and stay warm.

• This is a deductive argument.

• This is an inductive argument.

Explanation Slide...

Assuming that it is not Ray’s first Canadian winter, most likely he knows about Canadian winters, and what to expect weather-wise during that time of year. As a result, Ray is able to deduce (based on the fact that it is nearing winter,) that he’s going to need a new coat to keep warm. Ray used his deductive logic skills to arrive at the conclusion that he needs a new jacket for winter.

Multiple Choice

Noah wants to sign up for a triathlon, but he doesn't know how to swim. The triathlon involves swimming, so Noah can't sign up to compete unless he learns how to swim first.

• This is a deductive argument.

• This is a weak deductive argument.

• This is an inductive argument.

Explanation Slide...

In this case, Noah is able to deduce two important pieces of information by using his deductive reasoning skills: triathlons require swimming, and he needs to know how to swim if he is to compete in the triathlon. Through the ability to deduct from broader information, Noah is able to form the conclusion that if he is to compete in the triathlon, he has to learn how to swim first.

Multiple Choice

Susan wants to bake a cake, but she doesn't have any flour. Susan knows that to bake a cake, she needs flour. Since she has no flour, she cannot bake a cake.

• This is an inductive argument.

• This is a deductive argument.

Explanation Slide...

Susan may not be able to bake a cake, but at least she’s able to use her deductive reasoning skills to realize it. While it is not always apparent to the person that is utiliizing their deductive skills, Susan started with understanding a general claim about baking cakes—namely, that you need flour.Subsequently, she realized she had no flour; which then led her to ultimately conclude that she can’t bake a cake (all as a result of her ability to deduce information from a broad claim!)

Multiple Choice

The few rap songs that I've listened to included remarks that were inappropriate. Therefore, all rap music is inappropriate.

• This is a weak inductive argument.

• This is a strong inductive argument.

• This is a sound deductive argument.

Explanation Slide...

While rap music can certainly have some uncouth lyrics, it is surely not the case that rap music is inherently bad, or that every single rap song that exists is not acceptable. There are many rap musicians who rap positive lyrics.Therefore, this is an overgeneralization (often used by parents!) that aims to exclude the good with the bad, rather than taking a more nuanced look at the issue at hand.