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BEFORE WE READ CHAPTER 8….. All Cats are stupid. So if I have a cat, I know that it is….

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LEFT vs. RIGHT If C STUPID

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STIMULUS/RESPONSE Only people who have been tested can give blood. SO If Giving Blood YOU BE Tested

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Cause / Effect If there is a bail-out then millions of people will keep their homes. SO B H

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Sufficiency / Necessity In order to vote, a person has to be at least 18, registered, a resident, and NOT convicted of a felony. SO V 18 & Reg & Res & -F THE THING TO KEEP YOUR EYE ON HERE IS PROOF. If a person is 18, registered, a resident and not a felon, what do we know? BUT if we know that they VOTED, what do we know?

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WE CAN “CONTRAPOSE” THIS BY DOING 3 THINGS: 1. FLIP IT (CONVERSE) 2. NEGATE EVERYTHING 3. SWAP ANY “ands” & “ors” WE DO NOT HAVE ANY, SO WE ARE DONE! “If you are giving Blood (G) then you were tested (T).” GTGT TGTG-- SO IF YOU ARE NOT TESTED, YOU DID NOT GIVE BLOOD.

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Let’s try another one… “If Tom goes to the store or to the gym, Sally will eat a pie.” FIRST, WE re-write it in symbols: TS OR TGSP Then we Converse it: SP TS or TG NEGATE EVERYTHING: -SP-TS or -TG Turn “ands” to “ors”, and turn “ors” into “ands” -SP-TS AND -TG AND NOW WE ARE DONE!

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“If Tom goes to the store or to the gym, Sally will eat a pie.” TS OR TGSP IF Sally does NOT eat pie, we know that Tom DID NOT go to the store AND he did NOT go to the gym. If he HAD done EITHER, Sally would have eaten the pie, which she did not. -SP-TS AND -TG

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TRY THIS ONE: Symbolize & Contrapose “If it rains or it snows, I will not go jogging.” R or S-J J-R & -S

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TRY THIS ONE: Symbolize & Contrapose “No planes can take off unless the fog clears.” P-F F-P SO, I wake up this morning and before I open the curtains, I notice that I cannot hear ANY PLANES taking off from the airport. What will the sky look like when I draw back the shades?

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BUT FIRST…..

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What happens if I do NOT buy any Kiwis? If I buy bananas, I will also buy strawberries. If I do not buy bananas, then Kiwis will be purchased. If I buy strawberries then I buy grapes too. It is really freakin’ hard to tell…. Right now. BUT……

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Put it into SYMBOLS and then CONTRAPOSE…Take a minute… If I buy bananas, I will also buy strawberries. If I do not buy bananas, then Kiwis will be purchased. If I buy strawberries then I buy grapes too.

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If I buy bananas, I will also buy strawberries. If I do not buy bananas, then Kiwis will be purchased. If I buy strawberries then I buy grapes too. BS -S-B -BK -KB SG -G-S IF I GET “B” I HAVE TO GET “S”. AND if I have “S”, I have to have “G” So “B” gets me “S” and “S” gets me “G”…SO I CAN COMBINE THEM INTO A BIGGER RULE: BS & G

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-S-B -BK -KB SG -G-S -S gets me –B Does –B get me anything else? K

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K BY COMBINING THESE STIMULUS/RESPONSE RELATIONSHIPS, WE SEE THE DEEPER IMPLICATIONS OF THREE INITIALLY SIMPLE STATEMENTS

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K WHAT MUST BE TRUE IF: BANANAS ARE PURCHASED?

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K WHAT MUST BE TRUE IF: BANANAS ARE NOT PURCHASED?

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K WHAT MUST BE TRUE IF: STRAWBERRIES ARE NOT PURCHASED?

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K WHAT MUST BE TRUE IF: KIWIS ARE NOT PURCHASED?

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TRY FINDING OTHERS YOU CAN COMBINE! BS & G -S-B & K -BK -KB & S & G SG -G-S & -B & K WHAT MUST BE TRUE IF: GRAPES ARE PURCHASED?

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G-dawg Symbols: = “IF – THEN” = “AND” – = “NOT” V = “OR” D-dawg talks a lot about “truth tables” They CAN be useful tools for helping us to understand things. LET’S LOOK AT “IF – THEN”. If Tom eats beans he will have gas. B G B G B G T T T T F F F T T F F T All this table is doing is DEFINING the “ ” relationship: IF B IS TRUE THEN G IS ALSO TRUE.

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If Jason has a machete’ then Curtis will die. IN G-dawg SYMBOLS: JM CD CONTRAPOSITIVE: -CD -JM AND from this we know that the ONLY two things that PROVE anything for us are… A)JM & -JM B)CD & -CD C)JM & CD D)-CD & -JM E)JM & - CD

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Is this a valid argument? If determinism holds, people do not have free will. People have free will. Therefore determinism does not hold. D -F F -D F -D HOW CAN WE FIGURE THIS OUT? WHAT DO WE KNOW HOW TO DO? Put it into symbols CONTRAPOSE IT! HOW FREAKIN’ EASY IS THAT?

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Let’s try another one: If Christopher jacks the Blu-Ray truck he will make enough money to pay back his uncle Tony. Sadly he was not able boost the truck so he will not be able to pay Tony back. SYMBOLSContrapositive CJT $$$ -CJT - $$$ - $$$ - CJT

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Let’s up the ante…. A person who pulls their pork and eats cumquats either has carpal tunnel syndrome or head lice. Tony has carpal tunnel syndrome and head lice so he must either pull his pork or eat cumquats. SYMBOLS P EC C V L C L P V EC Contrapositive: -C -L -P V - EC

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LET’S GET SOME CANDY! Allison is going to the store to buy some candy. She has several kinds to choose from: Juicy Fruit, Kit-Kats, Licorice, Mentos, Nougat Bars, Oh-Henrys, and Paydays. (J,K,L,M,N,O,P) 28(c) 2008-2009 Brad Lord-Leutwyler

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THERE BE RULES FOR PICKING THE CANDY! 1. If she buys K, she does NOT buy any O. 2. If she buys M then she does NOT buy any N. 3. If she buys M, she buys at least one O. 4. If she buys any N, she buys at least one O. 5. If she buys any O then she buys P. 6. If she buys any P then she buys O. 7. If she buys any O, there are at least two of them. (c) 2008-2009 Brad Lord-Leutwyler29

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K -O O -K M -N N -M M O -O -M N O -O -N O P -P -O P O -O -P O at least 2 “O” -at least 2 “O” -O (c) 2008-2009 Brad Lord-Leutwyler30 1.If she buys K, she does NOT buy any O. 2.If she buys M then she does NOT buy any N. 3.If she buys M, she buys at least one O. 4.If she buys any N, she buys at least one O. 5.If she buys any O then she buys P. 6.If she buys any P then she buys O. 7.If she buys any O, there are at least two of them.

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K -O &-M & -N & -P O -K & P & @least 2 “O” M -N & O& -K & P & @least 2 “O” N -M &O& -K & P & @least 2 “O” M O &-N& -K & P & @least 2 “O” -O -M &-N&-P N O&–M & -K & P & @least 2 “O” -O -N & -M& -P O P & -K & @least 2 “O” -P -O & -M&-N P O& -K & P & @least 2 “O” -O -P & -M&-N O at least 2 “O” & -K & P -at least 2 “O” -O & -M &-N&-P (c) 2008-2009 Brad Lord-Leutwyler31 K -O O -K M -N N -M M O -O -M N O -O -N O P -P -O P O -O -P O at least 2 “O” -at least 2 “O” -O

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NOW LET’S SEE WHAT WE CAN DO WITH ALL OF THAT! K -O &-M & -N & -P O -K & P & @least 2 “O” M -N & O& -K & P & @least 2 “O” N -M &O& -K & P & @least 2 “O” M O & -K & P & @least 2 “O” -O -M &-N&-P N O&–M & -K & P & @least 2 “O” -O -N & -M& -P O P & -K & @least 2 “O” -P -O & -M&-N P O& -K & P & @least 2 “O” -O -P & -M&-N O at least 2 “O” -at least 2 “O” -O (c) 2008-2009 Brad Lord-Leutwyler32 If Allison wants to get as many different kinds of candy as possible, what is the one candy she MUST NOT buy? A)K B)L C)M D)N E)P

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K -O &-M & -N & -P O -K & P & @least 2 “O” M -N & O& -K & P & @least 2 “O” N -M &O& -K & P & @least 2 “O” M O & -K & P & @least 2 “O” -O -M &-N&-P N O&–M & -K & P & @least 2 “O” -O -N & -M& -P O P & -K & @least 2 “O” -P -O & -M&-N P O& -K & P & @least 2 “O” -O -P & -M&-N O at least 2 “O” -at least 2 “O” -O (c) 2008-2009 Brad Lord-Leutwyler33 If Allison does not buy any Paydays, then she could still get which of the following? A)J and K B)J and M C)K and M D)K and N E)L and O

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K -O &-M & -N & -P O -K & P & @least 2 “O” M -N & O& -K & P & @least 2 “O” N -M &O& -K & P & @least 2 “O” M O & -K & P & @least 2 “O” -O -M &-N&-P N O&–M & -K & P & @least 2 “O” -O -N & -M& -P O P & -K & @least 2 “O” -P -O & -M&-N P O& -K & P & @least 2 “O” -O -P & -M&-N O at least 2 “O” -at least 2 “O” -O (c) 2008-2009 Brad Lord-Leutwyler34 If Allison buys at least one piece of candy, what is the LEAST and the MOST number of different kinds she can buy? A)1,4 B)1,5 C)1,6 D)2,5 E)2,6

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K -O &-M & -N & -P O -K & P & @least 2 “O” M -N & O& -K & P & @least 2 “O” N -M &O& -K & P & @least 2 “O” M O & -K & P & @least 2 “O” -O -M &-N&-P N O&–M & -K & P & @least 2 “O” -O -N & -M& -P O P & -K & @least 2 “O” -P -O & -M&-N P O& -K & P & @least 2 “O” -O -P & -M&-N O at least 2 “O” -at least 2 “O” -O (c) 2008-2009 Brad Lord-Leutwyler35 What can NEVER BE TRUE? A)She gets exactly 4 candies, at least one of which is Juicy Fruit. B)She gets exactly four candies, at least one of which is Licorice. C)She gets exactly three candies, one of which is Mentos. D)She gets exactly three candies, at least one of which is an Oh-Henry. E)She gets exactly three candies, at least one of which is a Payday.

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FIN

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