Sherlock: ...my dear Watson. (A little later) Watson: Elementary.
However, this quote can be found in the 1929 film about Sherlock Holmes and has been made famous. A person that has never read Sir Arthur Conan Doyle but has seen this movie and heard the quote many times before may conclude that this phrase is said by Holmes repeatedly. This person has used inductive reasoning to come to this conclusion, though it is an incorrect conclusion.
Inductive reasoning is defined as"the process of forming conclusions on the basis of observations and experiments". The conclusions made through the use of inductive reasoning are not always true, as found in the example above. Here is a better example: "All sheep that I have seen are white, therefore all sheep are white." Again, this conclusion is wrong, but this does not mean that all conclusions made by inductive reasoning are wrong.
Another form of reasoning is deductive reasoning. Deductive reasoning is defined as "the process of deriving conclusions from given statements". With deductive reasoning, you are given a set of 'premises', or a general rule known to be true; with this set of premises, you can make a specific conclusion:
Premise: All men are mortal. Socrates is a man.
With these clues, I can deduce that Socrates is mortal.
A useful tool to see if conclusions are valid through your deductions is a Venn Diagram. This slideshow will help me to explain:
You can also use deductive reasoning to solve logic problems. Let's look at the following problem:
Use the given clues to match the jobs, majors, and method of transportations with the correct students
Students: Freshman, Sophomore, Junior, Senior
Work: Coffee Shop, Library, Theatre, Tutor
Major: English, Computer Science, Math, Psychology
Transportation: Bike, Bus, Car, Skateboard
A. The English major rides a bike
B. The tutor is a junior and won't ride a skateboard.
C. The sophomore takes the bus.
D. The freshman won't work in the coffee shop or drive a car.
E. The skateboarder is a psychology major.
F. The computer science major works in the library.
G. The math major works in the coffee shop and won't drive a car.
H. The senior drives a car.
Okay. So the first thing we want to do is to either create a chart, cut out slips of paper for each word, or any other sort of visual representation that works for you. I chose to create a chart. Then, you want to take each step one at a time, filling out any information given.
A. So, I pair English major and bike in the same column because of the first clue given.
B. I know that the junior is a tutor, and does not ride a skateboard, so I fill that out.
You can also use deductive reasoning to solve logic problems. Let's look at the following problem:
Use the given clues to match the jobs, majors, and method of transportations with the correct students
Students: Freshman, Sophomore, Junior, Senior
Work: Coffee Shop, Library, Theatre, Tutor
Major: English, Computer Science, Math, Psychology
Transportation: Bike, Bus, Car, Skateboard
A. The English major rides a bike
B. The tutor is a junior and won't ride a skateboard.
C. The sophomore takes the bus.
D. The freshman won't work in the coffee shop or drive a car.
E. The skateboarder is a psychology major.
F. The computer science major works in the library.
G. The math major works in the coffee shop and won't drive a car.
H. The senior drives a car.
Okay. So the first thing we want to do is to either create a chart, cut out slips of paper for each word, or any other sort of visual representation that works for you. I chose to create a chart. Then, you want to take each step one at a time, filling out any information given.
A. So, I pair English major and bike in the same column because of the first clue given.
Student | |
Work | |
Major | English |
Transportation | Bike |
B. I know that the junior is a tutor, and does not ride a skateboard, so I fill that out.
Student | Junior | |
Work | Tutor | |
Major | English | |
Transportation | Bike | (not a skateboard) |
C. I also know that the sophomore takes the bus.
Student | Junior | Sophomore | |
Work | Tutor | ||
Major | English | ||
Transportation | Bike | (not a skateboard) | Bus |
D. The freshman does not work in the coffee shop, and they do not ride a car. I know that the freshman will either ride the bike or the skateboard.
E. This is what my table would look like after reading the clues.
Student | Junior | Sophomore | Senior | ||||
Work | Tutor | Library | Coffee Shop | ||||
Major | English | Psychology | Computer Science | Math | |||
Transportation | Bike | (not skateboard) | Bus | Skateboard | Car |
G. Now, I go back to clue B. I know that the junior does not ride the skateboard. Because the senior rides the car and the sophomore rides the bus, the only other option is the bike. So, I combine the column with the bike and the English major into the column with the junior's information.
Student | Junior | Sophomore | Senior | |||
Work | Tutor | Library | Coffee Shop | |||
Major | English | Psychology | Computer Science | Math | ||
Transportation | Bike | Bus | Skateboard | Car |
F. Now I look at clue D. I knew that the freshman will either ride the bike or the skateboard. Now I know that the freshman rides the skateboard, so I will add freshman to that column.
Student | Junior | Sophomore | Senior | |||
Work | Tutor | Library | Coffee Shop | |||
Major | English | Psychology | Computer Science | Math | ||
Transportation | Bike | Bus | Skateboard | Car |
G. Now, clue G states that the math major does not drive a car, so I know that the math major is not the senior. It has to be the sophomore, because I already have a major for the junior and the freshman.
Student | Junior | Sophomore | Freshman | Senior | |
Work | Tutor | Coffee | Library | ||
Major | English | Math | Psychology | Computer Science | |
Transportation | Bike | Bus | Skateboard | Car |
H. This leaves the computer science major for the senior.
Student | Junior | Sophomore | Freshman | Senior |
Work | Tutor | Coffee | Library | |
Major | English | Math | Psychology | Computer Science |
Transportation | Bike | Bus | Skateboard | Car |
I. Now all that is left is the job for the freshman. For this, I will look at the list of jobs, and fill in the job that is left: theatre. I will also organize the information in order of freshman to senior.
Students | Freshman | Sophomore | Junior | Senior |
Work | Theatre | Coffee Shop | Tutor | Library |
Major | Psychology | Math | English | Computer Science |
Transportation | Skateboard | Bus | Bike | Car |
And this is the answer! So, remember that by taking one clue and one step at a time, we can use deductive reasoning to solve these logic problems. Sherlock Holmes would be proud!
For more practice on logic puzzles or fun puzzles to share with your students, click here!
