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### Course: Algebra (all content)>Unit 18

Lesson 9: Deductive and inductive reasoning

# Inductive & deductive reasoning

Sal discusses the difference between inductive and deductive reasoning by considering a word problem. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What is inductive
• Inductive reasoning is when you start with true statements about specific things and then make a more general conclusion. For example: "All lifeforms that we know of depend on water to exist. Therefore, any new lifeform we discover will probably also depend on water." A conclusion drawn from inductive reasoning always has the possibility of being false. If the possibility that the conclusion is wrong is remote, then we call it a strong inductive argument. If there's a reasonably good chance the conclusion is wrong, then we call it a weak inductive argument.
• Is most science based on inductive or deductive reasoning?
• I believe inductive as most facts are unknown
• Is it fair to say that deduction is a theorem and induction is a postulate?
• No. Both theorems and postulates are elements of deductive reasoning. Inductive reasoning is noticing a pattern and making an educated guess based on that pattern.

Here's the test. Do we know for certain that the population of the town will be higher in 2020 than it was in 2010? No -- the fact that the population has risen every ten years in the past is interesting, but if the factory in town shuts down or there is a natural disaster, then the population might well drop. Of course, you wouldn't be very observant if you failed to notice that the population has been steadily rising and that it is reasonable to assume that it won't stop now. But since there is no airtight logical proof that the population will go up, our reasoning is inductive and not deductive.
• R.I.P. that 2020 population
• Doesn't the example in this video involve Inductive AND Deductive reasoning? Because inductive reasoning is used to make a generalization about the rate of population change. But then Deductive reasoning is used to draw specific information from the generalization just made. What am I missing?
• I do see your point there. Thing is, you've got to remember what deductive reasoning is; I guess the easiest way of putting it would be that it's the reverse of inductive. Inductive reasoning starts from the bottom to the top (in this case, 1950 to 2020), and deductive reasoning goes from the top back to the bottom.
We can only make a generalization about the future, but to make a prediction about history would use deductive reasoning since we know there was a decrease every year. However, I do like your thinking!
• How do you use both types of reasoning
• so deductive reasoning is using the given facts to make new more understandable facts?
• You got it. When we study deductive reasoning, we learn that we have to be careful to avoid guessing or new ambiguity, we must stick to fact.
(1 vote)
• So basically inductive reasoning has to be proved with facts and deductive reasoning is already proved but adds info?
• Deductive reasoning does not add to our store of knowledge; it merely rearranges it. Inductive involves some degree of guessing.
All teenagers like to watch TV. I am a teenager, therefore I like to watch TV (deductive)
Most teenagers like to watch TV. My cousin is a a teenager, therefore he probably likes to watch TV (inductive)
• A group of 50 friends meet for lunch. They greet each other by exchanging fist bumps. How many fist bumps are exchanged if each friend must bump with each of the 49 others?
(1 vote)
• how do you know what to do after you determine wether you'll use inductive or deductive
(1 vote)

## Video transcript

Think about this real world problem. To estimate the population of a town in upcoming years, one of the town workers collected populations from past years and made this table. So they have years starting with 1950 and going up by increments of 10 years. And they just figure out the population of the town in each of those years. The town wants to estimate the population for 2015, 2018, and 2020. To do this, will you be using inductive reasoning or deductive reasoning? Now before answering that, let's just think about what inductive reasoning is and what deductive reasoning is. Inductive reasoning is looking for a pattern or looking for a trend. So it's looking for a trend or a pattern and then generalizing. You could imagine, it's kind of extrapolating the information you have, generalizing. Deductive reasoning is taking some set of data or some set of facts and using that to come up with other, or deducing some other, facts that you know are true. When you generalize you don't know necessarily whether the trend will continue, but you assume it will. You don't know 100% it'll be true. With deductive reasoning, you know it'll be true. You're starting with facts. And then you're deducing other facts from those facts. Other facts that you know are true. Now, when the town is estimating, and that's kind of a clue that they're not going to know the exact population for 2015, 2018, and 2020. But when they estimate the population for these years, these years are in the future. They don't know what the population will be in those years. The best they can do is see the trend of growth here, maybe see what percentage it's growing every 10 years. Or what the absolute number of growth is every 10 years. And maybe they can continue that trend out to 2015, 2018, and 2020. So they'll be looking for trend in growth over this 60-year period. And then they'll generalize it out to these years. So this will be inductive reasoning.