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INTRODUCTION TO VENN DIAGRAMS Introduction to Venn Diagrams S P 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. Introduction to Venn Diagrams S P This In a Venn is a Venn diagram, diagram we consider for two terms. the relationship We can conceive between of two everyterms, element or groups. of S as being We overlapthe within each boundary circle toofmake the Ssure circle. weEverything consider every which logical is notpossibility. an S is found Foroutside any thing thein the S circle. universe, it will be somewhere on this Venn diagram. Introduction to Venn Diagrams x S P Inthe If a Venn thing diagram, is neither weinconsider S nor in the P, then relationship it is placed between outsidetwo of both terms, circles. 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. Introduction to Venn Diagrams x S P 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. Introduction to Venn Diagrams x S P 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. Introduction to Venn Diagrams x S P 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. Introduction to Venn Diagrams x S P 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. Introduction to Venn Diagrams S P 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. Introduction to Venn Diagrams S P In the a categorical Venn diagram statement above,we everything are sayingissomething blank. This about meansthe that S circle, I don’tspecifically have any whether anyabout information regionthe is empty relationship or elsebetween has something S and P.inItit.does It can’t not be mean both, that butthe weareas might are empty. not know A blank which space onesimply it is. When means wethat leave myan information area blank,orthat knowledge just means about that we don’t the givenknow area iswhether “empty”. there Theisarea an element could beinempty, it, or else or itiscould empty. have something in it. Introduction to Venn Diagrams 1 S 2 3 P In the we Since Venn arediagram saying something above, everything about the is blank. subject This term, means we will thatconcentrate I don’t haveon any the S circle. The Sabout information circle has the two relationship regions,between one which S and is outside P. It does of P,not andmean one which that the is inside areas of P.empty. are We canAsay blank about space a region simplythat means it is either that my empty, information or that or it has knowledge something about in it. So, that the givengives areaus is “empty”. a total of four The area things could we can be empty, say. Let’s or number it could have each something region. in it. Introduction to Venn Diagrams 1 S 2 3 P Since We can wesay areabout saying region something one either about that theitsubject is empty, term, or that we will it has concentrate somethingon in the it. To S say that circle. The it isSempty, circle has wetwo shade regions, in theone entire which region. is outside Click the of P,mouse and one to fill which in area is inside 1. Click of P. We again cantosay seeabout whataitregion looks like thattoit say is either that region empty,1or is that not empty. it has something in it. So, that gives us a total of four things we can say. Let’s number each region. Introduction to Venn Diagrams 1 2 3 x S P 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. Introduction to Venn Diagrams 1 x S 2 3 x P To show We can say that about area region two is empty, one either we that can shade it is empty, it. Click or that the mouse it has something to show that in it. area To say 2 is empty. that it isClick empty, thewe mouse shade again in the toentire show region. that areaClick 2 is the not mouse empty.to fill in area 1. Click again to see what it looks like to say that region 1 is not empty. Introduction to Venn Diagrams 1 2 3 x S P So,show To therethat are four area things two is we empty, can say we can about shade S in it. comparison Click the mouse to P. We tocan show saythat thatarea the 2 is empty. area of S outside Click the of Pmouse is empty, again or that to show it has that something area 2 is in not it.empty. 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. Introduction to Venn Diagrams 1 2 S “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 3 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 2 S “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 3 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 2 S “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 3 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 2 3 x S “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 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 2 3 x S “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 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 2 S “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 3 P Click the statements to see the Venn diagram for each. Click here to move on. Introduction to Venn Diagrams 1 S 2 3 P Congratulations! You have now been introduced to Venn diagrams for categorical statements. Hopefully you will find them useful.