which is just evaluating information and making appropriate judgments
Think about how you get dressed in the morning. What you wear depends on a number of different factors. What will the weather be like that day? Will it be hot or cold? Is it going to rain? Will you be going into the office or doing something else? Let's say, for example, that it is winter and it is a Saturday. During the winter, it is cold, and on Saturdays you take your dog to the park. Based on this information [the data], you can say with a good amount of certainty that you will need to wear cold-weather clothing, such as warm socks, long pants, and a coat. You will also need to plan for being outside, so you decide to wear a hat, gloves, and maybe even a scarf.
What about when you make lunch? Here, you need to consider what food you have in your fridge, how much time you have to cook, what you already ate for breakfast [because who wants to eat the same meal twice in a row?], as
well as if you have dietary restrictions [like being a vegetarian]. Based on all of this information, you can come to a logical conclusion about what to have for lunch that day.
These are, of course, very simple examples. But, can you see how pieces of information take on new meaning when you put them into context and draw some conclusions from them?
Let's say you ran an experiment to better understand plant growth. You had three groups of plants: one that received fertilizer and two
that did not. One of the non-fertilized groups received three more hours of sunlight exposure than the other two groups of plants, and the third group of plants received nothing. In the end, the group that received the fertilizer had the greatest amount of growth, the group that received neither fertilizer nor extra sunlight had the least amount of growth, and the group that received no fertilizer, but did receive extra sunlight was somewhere in between.
What conclusions might you draw from
these results? You might say that both fertilizer and sunlight led to an increase in plant growth since both of these groups grew more than the group that received nothing. You might also conclude that fertilizer had a greater impact on growth than sunlight, since the fertilizer group grew more than the extra sunlight group.
Based on the preliminary data, these conclusions make sense. But now your results are so much more meaningful because, instead of just presenting some arbitrary plant
growth values, you have explained what the numbers mean in a given context. Additionally, you might also conclude that further studies are still needed because now you have more questions. Such future studies might test whether different types of fertilizers affect plant growth differently, or if the amount of fertilizer plays a role in plant growth. You might also test sunlight alone [leaving fertilizer out of the experiment] to determine the optimal amount of extra sunlight for maximum plant
growth.
Inductive Reasoning
what is characterized by drawing a general conclusion
[making a conjecture]
from repeated observations of specific examples. The conjecture may or may not be true.
A Counter Example
what is a single example that does not support the conjecture. This proves that the conjecture is false.
Deductive Reasoning
___is characterized by applying general principles
to specific examples.
conjecture
counterexample
Say I flip a coin ten times, and it lands heads up every time. I might make the ______"This coin always lands heads up." But if the eleventh flip lands tails up, then that flip would be the ________ that proves my conjecture false.
specific example
general principle
If someone asks me, "What is the voltage drop across this 100 ohm resistor if there are 2 amps of current running through it?" I would find the voltage for this _____ by using the _____
voltage = current times resistance
voltage = 2 · 100
voltage = 200 volts.
Inductive reasoning
What
can only lead to a probable [or more likely]
result?
Inductive reasoning
What cannot lead to a 100% certain answer?
Deductive Reasoning
If used properly ___ will lead to a 100% correct
answer.
A Premise
___can be an assumption, law, rule,
widely held idea, or
observation
A Conclusion
___follows from the premises by inductive or deductive
reasoning.
A Logical Argument
__ made up of the premises and the conclusion.
Premises: "I am wearing clothes." "All of you are wearing clothes."
Conclusion: "Everyone in
Pennsylvania is wearing clothes."
This argument draws a very general conclusion from two specific
examples, so it is an inductive argument.
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used.
I am wearing clothes. All of you are wearing clothes. Therefore, everyone in Pennsylvania is wearing clothes.
Premises: "All humans need air to live." "I am a
human."
Conclusion: "I need air to live."
This argument applied the general principle that all humans need air to a specific example, me, so it is a deductive argument.
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used.
All humans need air to live. I am a human. I need air to live.
Premises: "I have 7 apples." "I buy 3 more apples."
Conclusion: "I
now have 10 apples."
This argument applied the general principle of addition to a specific example, 7 + 3 = 10 apples, so it is a deductive argument
Identify the premises and conclusion and determine whether deductive or inductive reasoning was used.
I have 7 apples. I buy 3 more apples. I now have 10 apples.
Inductive reasoning is not 100% accurate
_____ reasoning is not 100% accurate.
Each number increases by 2, and this is a list of odd numbers. So 7 + 2 = 9 is the most probable next term.
What is the most probable next term?
1, 3, 5, 7
Each number increases by 12, and this is a list of odd numbers. So
41 + 12 = 53 is the most probable next term.
What is the most probable next
term?
5, 17, 29, 41
True
True or False
There may be multiple correct explanations for the same pattern
Conjecture
An educated guess based on repeated observations of a particular process or pattern.
Which of the following are properties of inductive arguments? Select all that apply.
It cannot prove its conclusion true. At best, it shows that its conclusion probably is true.
It can be analyzed only in terms of its strength.
A conclusion is formed by generalizing from a set of more specific premises.
Which of the following are properties of deductive arguments? Select all that apply.
A specific conclusion is deduced from a set of more general [or equally general] premises.
It can be analyzed in terms of its validity and soundness. It is valid if its conclusion follows necessarily from its premises. It is sound if it is valid and its premises are true.
It can be valid even when its conclusion is blatantly false.
Determine whether the reasoning is an example of deductive or inductive reasoning.
In the sequence 9, 12, 15, 18, 21, ..., the most probable next
term is 24.
The reasoning is deductive because general principles are being applied to specific examples.
The reasoning is inductive because general principles are being applied to specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
Determine whether the reasoning is an example of deductive or inductive reasoning.
It is a fact that every student who ever attended Delgado University was accepted into graduate school. Because I am attending Delgado University, I can expect to be accepted to graduate school, too.
The reasoning is inductive because general principles are being applied to specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is deductive because general principles are being applied to specific examples.
The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
If you build it, they will come. You build it. Therefore, they will come.
Choose the correct answer below.
A.
The reasoning is deductive because general principles are being applied to specific examples.
B.
The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
C.
The reasoning is inductive because
general principles are being applied to specific examples.
D.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
The reasoning is deductive because general principles are being applied to specific examples.
It has rained every day for the past six days, and it is raining today as well. So it will also rain tomorrow.
Choose the correct
answer below.
A.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
B.
The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
C.
The reasoning is deductive because general principles are being applied to specific examples.
D.
The reasoning is inductive because general principles are being applied to specific examples.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
If the mechanic says that it will take seven days to repair your SUV, then it will actually take ten days. The mechanic says, "I figure it'll take exactly one week to fix it, ma'am." Then you can expect it to be ready ten days from now.
Choose the correct answer below.
A.
The reasoning is deductive
because general principles are being applied to specific examples.
B.
The reasoning is deductive because a general conclusion is being made from repeated observations of specific examples.
C.
The reasoning is inductive because a general conclusion is being made from repeated observations of specific examples.
D.
The reasoning is inductive because general principles are being applied to specific examples.
A.
The reasoning is deductive
because general principles are being applied to specific examples.
Your answer is correct.
Which of the following are examples of inductive arguments? Select all that apply.
A.
Premise:
[−2]×[3]=−6
Premise:
[−3]×[1]=−3
Premise:
[−4]×[2]=−8
Conclusion:
The product of two negative numbers is negative.
B.
Premise:
[-2]×[3]=−6
Premise:
[−3]×[1]=−3
Premise:
[−4]×[2]=−8
Conclusion:
The
product of a negative number and a positive number is negative.
C.
Premise:
If a figure is a triangle, then it has three sides.
Premise:
Squares have four sides.
Conclusion:
Squares are not triangles.
D.
Premise:
No country is an island.
Premise:
Iceland is an island.
Conclusion:
Iceland is not a country.
Premise:
[−2]×[3]=−6
Premise:
[−3]×[1]=−3
Premise:
[−4]×[2]=−8
Conclusion:
The
product of a negative number and a positive number is negative.
Which of the following are examples of inductive arguments? Select all that apply.
A.
Premise:
[−2]×[3]=−6
Premise:
[−3]×[1]=−3
Premise:
[−4]×[2]=−8
Conclusion:
The product of two negative numbers is negative.
B.
Premise:
[-2]×[3]=−6
Premise:
[−3]×[1]=−3
Premise:
[−4]×[2]=−8
Conclusion:
The product of a
negative number and a positive number is negative.
C.
Premise:
If a figure is a triangle, then it has three sides.
Premise:
Squares have four sides.
Conclusion:
Squares are not triangles.
D.
Premise:
No country is an island.
Premise:
Iceland is an island.
Conclusion:
Iceland is not a country.
C.
Premise:
If a figure is a triangle, then it has three sides.
Premise:
Squares have four
sides.
Conclusion:
Squares are not triangles.
D.
Premise:
No country is an island.
Premise:
Iceland is an island.
Conclusion:
Iceland is not a country.
Determine the most probable next term in the list of numbers.
6, 9, 12, 15, 18
21
Determine the most probable next term in the list of numbers.
one half
1/2,
3/4,
5/6,
7/8
9/10
11/12
Determine the most probable next term in the following list of numbers.
2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2
2