WELCOME! Pretty Please! Phones off, iClickers out, brains active

WELCOME! WELCOME! Pretty Please! Phones off, iClickers out, brains active.

TRY THIS ONE:TRY THIS ONE:Symbolize & ContraposeSymbolize & Contrapose

“No planes can take off unless the fog clears.”

P -F

F -PSO, 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?

What happens if I do NOT buy What happens if I do NOT buy any Kiwis?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……

Put it into SYMBOLS and then Put it into SYMBOLS and then CONTRAPOSE…Take a CONTRAPOSE…Take a minute…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.

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.

B S-S -B-B K-K BS G-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:

BB S & GS & G

B S & G-S -B -B K-K BS G-G -S

-S gets me –B Does –B get me anything else?

K

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

BY COMBINING THESE STIMULUS/RESPONSE RELATIONSHIPS, WE SEE THE DEEPER IMPLICATIONS OF THREE INITIALLY SIMPLE STATEMENTS

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

WHAT MUST BE TRUE IF:

BANANAS ARE PURCHASED?

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

WHAT MUST BE TRUE IF:

BANANAS ARE NOT PURCHASED?

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

WHAT MUST BE TRUE IF:

STRAWBERRIES ARE NOT PURCHASED?

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

WHAT MUST BE TRUE IF:

KIWIS ARE NOT PURCHASED?

TRY FINDING OTHERS YOU CAN TRY FINDING OTHERS YOU CAN COMBINE!COMBINE!

B S & G-S -B & K -B K-K B & S & GS G-G -S & -B & K

WHAT MUST BE TRUE IF:

GRAPES ARE PURCHASED?

G-dawg Symbols: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 GT T TT F FF T TF F T

All this table is doing is DEFINING the “” relationship: IF B IS TRUE THEN G IS ALSO TRUE.

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 & -JMB)CD & -CDC)JM & CDD)-CD & -JME)JM & - CD

Is this a valid argument?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?

Let’s try another one: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.

SYMBOLS Contrapositive

CJT $$$ -CJT- $$$

- $$$ - CJT

Let’s up the ante….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

LET’S GET SOME CANDY!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)

18(c) 2008-2009 Brad Lord-Leutwyler

THERE BE RULES FOR THERE BE RULES FOR PICKING THE CANDY!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-Leutwyler 19

K -OO -KM -NN -MM O-O -MN O-O -NO P-P -OP O-O -PO at least 2 “O”-at least 2 “O” -O

(c) 2008-2009 Brad Lord-Leutwyler 20

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.

K -O &-M & -N & -PO -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&-PN O&–M & -K & P & @least 2

“O”-O -N & -M& -PO P & -K & @least 2 “O”-P -O & -M&-NP O& -K & P & @least 2 “O”-O -P & -M&-NO at least 2 “O” & -K & P-at least 2 “O” -O & -M &-N&-

P(c) 2008-2009 Brad Lord-Leutwyler 21

K -OO -KM -NN -MM O-O -MN O-O -NO P-P -OP O-O -PO at least 2 “O”-at least 2 “O” -O

NOW LET’S SEE WHAT WE NOW LET’S SEE WHAT WE CAN DO WITH ALL OF THAT!CAN DO WITH ALL OF THAT!

K -O &-M & -N & -PO -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&-PN O&–M & -K & P &

@least 2 “O”-O -N & -M& -PO P & -K & @least 2 “O”-P -O & -M&-NP O& -K & P & @least 2

“O”-O -P & -M&-NO at least 2 “O”-at least 2 “O” -O

(c) 2008-2009 Brad Lord-Leutwyler 22

If Allison wants to get as many different kinds of candy as possible, what is the one candy she MUST NOT buy?A)KB)LC)MD)NE)P

K -O &-M & -N & -PO -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&-PN O&–M & -K & P &

@least 2 “O”-O -N & -M& -PO P & -K & @least 2 “O”-P -O & -M&-NP O& -K & P & @least 2

“O”-O -P & -M&-NO at least 2 “O”-at least 2 “O” -O

(c) 2008-2009 Brad Lord-Leutwyler 23

If Allison does not buy any Paydays, then she could still get which of the following?A)J and KB)J and MC)K and MD)K and NE)L and O

K -O &-M & -N & -PO -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&-PN O&–M & -K & P &

@least 2 “O”-O -N & -M& -PO P & -K & @least 2 “O”-P -O & -M&-NP O& -K & P & @least 2

“O”-O -P & -M&-NO at least 2 “O”-at least 2 “O” -O

(c) 2008-2009 Brad Lord-Leutwyler 24

If Allison buys at least one piece of candy, what is the LEAST and the MOST number of different kinds she can buy?A)1,4B)1,5C)1,6D)2,5E)2,6

K -O &-M & -N & -PO -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&-PN O&–M & -K & P &

@least 2 “O”-O -N & -M& -PO P & -K & @least 2 “O”-P -O & -M&-NP O& -K & P & @least 2

“O”-O -P & -M&-NO at least 2 “O”-at least 2 “O” -O

(c) 2008-2009 Brad Lord-Leutwyler 25

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.

FINFIN