INTRODUCTION TO VENN DIAGRAMS Introduction to Venn Diagrams

Introduction to Venn Diagrams S P This is a Venn diagram for two terms.

Introduction to Venn Diagrams S P This In a Venn is a Venn diagram,

Introduction to Venn Diagrams x S P Inthe If a Venn thingdiagram, is neither

Introduction to Venn Diagrams x S P If the thing is neither in S

Introduction to Venn Diagrams S P In a categorical statement we are saying something

Introduction to Venn Diagrams S P In the a categorical Venn diagram statement above,

Introduction to Venn Diagrams 1 S 2 3 P In the we Since Venn

Introduction to Venn Diagrams 1 S 2 3 P Since We can wesay areabout

Introduction to Venn Diagrams 1 2 3 x S P We can say about

Introduction to Venn Diagrams 1 x S 2 3 x P To show We

Introduction to Venn Diagrams 1 2 3 x S P So, show To therethat

Introduction to Venn Diagrams 1 2 S “Area 1 is empty” corresponds to All

Introduction to Venn Diagrams 1 2 3 x S “Area 1 is empty” corresponds

Introduction to Venn Diagrams 1 S 2 3 P Congratulations! You have now been

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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 every terms, element or groups. of S as We being overlapthe within each boundary circle toofmake the Ssure circle. we. Everything 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 thingdiagram, is neither weinconsider S nor in P, thethen 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. If it is a P, but not an S, then it goes in the right crescent-shaped region.

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 whethere 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. Thisabout meansthe that S circle, I don’tspecifically have any whether anyabout information regionthe is empty relationship or elsebetween has something S and P. in Itit. does It can’t notbe mean both, that butthe weareas might are empty. not know A blank which space onesimply it is. When means wethat leave myaninformation area blank, or that 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 that concentrate I don’t haveonany the S circle. The Sabout information circle the has relationship two 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 can. Asay blank about space a region simplythat means it is that either my empty, information or thator it has knowledge something about in it. So, that the givengives areaus is “empty”. a total of four The things area 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. The circle. it is. Sempty, 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 what aitregion looks like thattoitsay is either that region empty, 1 or is not thatempty. 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 is. Click empty, thewe mouse shadeagain in the toentire show region. that area. Click 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 areathings two is we empty, can say we can about shade S in it. comparison Click the mouse to P. We to can show say that area 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 All S are P “Area 2 is empty” corresponds to No S are P “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. Some S are P Some S are not P

Introduction to Venn Diagrams 1 2 3 x S “Area 1 is empty” corresponds to All S are P “Area 2 is empty” corresponds to No S are P “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. Some S are P Some S are not P

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.