2. Introduction to Venn Diagrams SP This is a Venn diagram for two terms. We can conceive of every element of S as being within the boundary of the S circle. Everything which is not an S is found outside the S circle.

3. Introduction to Venn Diagrams SP In a Venn diagram, we consider the relationship between two terms, or groups. We overlap each circle to make sure we consider every logical possibility. For any thing in the universe, it will be somewhere on this Venn diagram. This is a Venn diagram for two terms. We can conceive of every element of S as being within the boundary of the S circle. Everything which is not an S is found outside the S circle.

4. Introduction to Venn Diagrams SP If the thing is neither in S nor in P, then it is placed outside of both circles. x In a Venn diagram, we consider the relationship between two terms, or groups. We overlap each circle to make sure we consider every logical possibility. For any thing in the universe, it will be somewhere on this Venn diagram.

5. Introduction to Venn Diagrams SP If the thing is neither in S nor in P, then it is placed outside of both circles. x If the thing is an S, but not a P, then it would go in the left crescent-shaped region.

6. Introduction to Venn Diagrams SP If the thing is neither in S nor in P, then it is placed outside of both circles. x If the thing is an S, but not a P, then it would go in the left crescent-shaped region. If it is a P, but not an S, then it goes in the right crescent-shaped region.

7. Introduction to Venn Diagrams SP If the thing is neither in S nor in P, then it is placed outside of both circles. x If the thing is an S, but not a P, then it would go in the left crescent-shaped region. If it is a P, but not an S, then it goes in the right crescent-shaped region. Finally, the center “football” region is reserved for things which are both S and P.

8. Introduction to Venn Diagrams SP If the thing is neither in S nor in P, then it is placed outside of both circles. If the thing is an S, but not a P, then it would go in the left crescent-shaped region. If it is a P, but not an S, then it goes in the right crescent-shaped region. Finally, the center “football” region is reserved for things which are both S and P. x

9. Introduction to Venn Diagrams SP In a categorical statement we are saying something about the S circle, specifically whether any region is empty or else has something in it. It can’t be both, but we might not know which one it is. When we leave an area blank, that just means that we don’t know whether there is an element in it, or else is empty.

10. Introduction to Venn Diagrams SP In a categorical statement we are saying something about the S circle, specifically whether any region is empty or else has something in it. It can’t be both, but we might not know which one it is. When we leave an area blank, that just means that we don’t know whether there is an element in it, or else is empty. In the Venn diagram above, everything is blank. This means that I don’t have any information about the relationship between S and P. It does not mean that the areas are empty. A blank space simply means that my information or knowledge about the given area is “empty”. The area could be empty, or it could have something in it.

11. Introduction to Venn Diagrams SP Since we are saying something about the subject term, we will concentrate on the S circle. The S circle has two regions, one which is outside of P, and one which is inside of P. We can say about a region that it is either empty, or that it has something in it. So, that gives us a total of four things we can say. Let’s number each region. 1 2 3 In the Venn diagram above, everything is blank. This means that I don’t have any information about the relationship between S and P. It does not mean that the areas are empty. A blank space simply means that my information or knowledge about the given area is “empty”. The area could be empty, or it could have something in it.

12. Introduction to Venn Diagrams SP 1 2 3 We can say about region one either that it is empty, or that it has something in it. To say that it is empty, we shade in the entire region. Click the mouse to fill in area 1. Click again to see what it looks like to say that region 1 is not empty. Since we are saying something about the subject term, we will concentrate on the S circle. The S circle has two regions, one which is outside of P, and one which is inside of P. We can say about a region that it is either empty, or that it has something in it. So, that gives us a total of four things we can say. Let’s number each region.

13. Introduction to Venn Diagrams SP 1 2 3 We can say about region one either that it is empty, or that it has something in it. To say that it is empty, we shade in the entire region. Click the mouse to fill in area 1. Click again to see what it looks like to say that region 1 is not empty. x

14. Introduction to Venn Diagrams SP 1 2 3 We can say about region one either that it is empty, or that it has something in it. To say that it is empty, we shade in the entire region. Click the mouse to fill in area 1. Click again to see what it looks like to say that region 1 is not empty. x To show that area two is empty, we can shade it. Click the mouse to show that area 2 is empty. Click the mouse again to show that area 2 is not empty. x

15. Introduction to Venn Diagrams SP 1 2 3 To show that area two is empty, we can shade it. Click the mouse to show that area 2 is empty. Click the mouse again to show that area 2 is not empty. x So, there are four things we can say about S in comparison to P. We can say that the area of S outside of P is empty, or that it has something in it. We could also say that the area of S inside of P is either empty or has something in it. Each one of these statements has a simple English counterpart, which we will see in the next slide.

16. Introduction to Venn Diagrams SP 1 2 3 “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to Click the statements to see the Venn diagram for each. Click here to move on. Click here

17. Introduction to Venn Diagrams SP 1 2 3 Click the statements to see the Venn diagram for each. Click here to move on. Click here “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to

18. Introduction to Venn Diagrams SP 1 2 3 Click the statements to see the Venn diagram for each. Click here to move on. Click here “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to

19. Introduction to Venn Diagrams SP 1 2 3 Click the statements to see the Venn diagram for each. Click here to move on. Click here “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to x

20. Introduction to Venn Diagrams SP 1 2 3 Click the statements to see the Venn diagram for each. Click here to move on. Click here “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to x

21. Introduction to Venn Diagrams SP 1 2 3 Click the statements to see the Venn diagram for each. Click here to move on. “Area 1 is empty” corresponds to “Area 2 is empty” corresponds to “Area 2 has at least one element” corresponds to “Area 1 has at least one element” corresponds to

22. Introduction to Venn Diagrams SP 1 2 3 Congratulations! You have now been introduced to Venn diagrams for categorical statements. Hopefully you will find them useful.