Thursday, December 18, 2008

Using Venn Diagrams in Word Problems

In class today, we went over some questions on Venn diagram sets. You can see the answers to in the slides that Mr. K posted.

After doing a bit of that, we then learned how to apply our knowledge of Venn diagram sets and rules to problems that you would see in real life.

Let's see how we would solve problems that look like this with Venn diagrams:

"In a group of students 12 are taking chemistry, 10 are taking physics, 3 are taking both and 5 are taking neither. How many students are in the group?"

First we would draw our 'universe' and the Venn diagram that goes in it.:
('U' being universe, 'C' being chemistry, and 'P' being physics)

After you have everything set up, it's time to add in some numbers. Let's start with the easiest possible ones first.

Seeing how there are 5 students who aren't taking either chemistry or physics, we can tell right away that they're going to be placed somewhere in the 'universe', outside of the Venn diagrams.

The 3 students who are taking both courses are th
e next obvious choice. Since they are taking chemistry AND physics, they belong in the intersection, where the 'C' and the 'P' circle meet.

Now we'll figure out how many students are taking each course.

Automatically your brain might think that the number of students taking chemistry is 12 and the number of students taking physics is 10, but neither statement is true.

The actual number of students taking chemistry is 9, and the number of students taking physics is 7. Why? Because we exclude the 3 students that are taking both courses.

We subtract those 3 students from the pool of students taking chemistry (12 - 3 = 9) and physics (10 - 3 = 7).

We do this because in circles 'C' and 'P', we only want the number of students who are ONLY taking either chemistry or physics, excluding the students that are taking both.

Using the information we've gathered, we can determine the total number of students by adding up all the numbers. You should then finish off with this:
And that's how you solve a word problem with a Venn diagram.

We did a couple more examples, which all use pretty much the same procedure.

We did however, do one that involved 3 circles in the Venn diagram instead of 2. It seemed a little confusing, but solving it involved the same procedures as the previous examples. You just had to be very careful with your numbers.

That's about it for my scribe post, thanks for reading. The next scribe will be..camiLLe


Jeamille said...

aren't there 24 students in the group?

"ੴ KHALSA ੴ" said...

According to me Total num of students in the group=22

Anonymous said...