Venn Diagrams 1= s that are not p; 2= s that are p; 3= p that are not s 2 3 1 S P

Universal Propositions No S are P All S are P

Particular Propositions Some S are P Some S are not P X X P S P S

Syllogism Diagrams S= Smokers; P= Philosophers S P M= Musicians 1: Smokers that are not Philosophers or Musicians 3 2 1 2: Non-Musician Philosophers 5 who smoke. 4 3: Non-Musician Philosophers 6 who don’t smoke 4: Musicians who smoke and 7 who are not Philosophers 5: Musician Philosophers who smoke M 6: Musician Philosophers who don’t smoke. 7: Non-smoking Musicians who aren’t Philosophers

The Venn Diagram Validity Test Diagram information from premises and inspect to see if the conclusion is implied; if so, valid argument. 1. Enter marks (shading or “x”) only for premises, not for the conclusion. 2. Enter marks for universal premise first, if one is particular. 3. When entering information, focus on the two circles involved 4. The area where “x” goes is divided into two parts, if one part is shaded, put “x” in the other part; if both parts are unshaded, put “x” on the line.

Venn Diagram, example 1 No critical thinkers are cultists. All Applewhite followers are cultists. \ No Applewhite followers are critical thinkers. A T Valid C