Accepted Answer

Hi there!

In your own words, explain what is meant by “inductive reasoning” and “deductive reasoning”. State the differences between the two and provide examples to illustrate

Deductive reasoning takes all of the given facts and uses them and nothing else to form a conclusion.

For example, if you are given the statement: any number that ends with 5 is divisible by 5. Then you are given the number 755. You know, by deduction, that since 755 ends in 5, it is divisible by 5.

Inductive reasoning takes the given facts and adds inferences and interpretations to form a conclusion.

For example, if you feel some ice, you know it is cold. Then you are presented with a new batch of ice. By induction, you can reason that the new ice will be cold, too. There is no "given" that ice is cold, but you have inferred it.

Another inductive example. You are told that 755, 985, and 1035 are all divisible by 5. Then you are given 1025. Based on induction, you can see the pattern that perhaps if a number ends in 5, it is divisible by 5.



What is the purpose of estimation? Discuss advantages and disadvantages of relying on estimation. Provide an example of estimation used in your daily life

Estimation is important for coming to quick answers about problems. When you use estimation, you don't have to rely on calculators or computers. A problem with estimation is that you don't get an exact answer. That could be a problem, if for example, you are on an old elevator with a person limit, and you estimate too high for the number of people on it.

Estimation examples from our daily lives:

For example, when you go on the city bus, you may not want to count how many people there are exactly, but you can estimate within the nearest 10 or so.

When you are at the grocery store, you can estimate how much your final bill will be using estimation -- you can round each item's price to the nearest dollar and then add those estimated prices. Of course, you will not get the exact answer, but you will get close.

Let me know if you have any questions,
Scott

Expert:	Scott
Pos. Feedback:	100.0 %
Accepts:	5286
Answered:	8/7/2008

MIT Graduate

College degree in math... proficient in all levels -- from algebra to calculus