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Pizza Test

THE LOOLOOLO WAITERS PIZZA ORDER TEST

Cooks at the Looloolo Pizza Parlor do not understand our illogical English.
So they require their waiters to fill out a 3 circle diagram when a customer orders a pizza.
They use only 3 toppings for their pizzas: Anchovies, Beef, and Chicken.

Let A = I want a pizza with Anchovies = I want an Anchovy pizza.
Let B = I want a pizza with Beef = I want a Beef pizza.
Let C = I want a pizza with Chicken = I want a Chicken pizza.

You have applied to be a waiter at the Looloolo Pizza Parlor.
You are tested on your ability to fill out order diagrams
and write orders logically that Looloolos can understand.
Sometimes a customer lets the cooks decide which pizzas bake quicker.
That's why so many OR statements are on the test.

 

 

ASSIGNMENT

Translate ONE of the exercises below into set notation.
You must choose from the first 20 exercises until all 20 are translated.
In the applet at the top of this page,
click in those regions of the diagram that correspond to your notation.
Enter the order number and your notation into the applet's yellow text box.
Hoversanp, attach, and insert your diagram into a comment below.
Use the same format you have before to name and insert your picture file:
files/Pix/Plato-pizzatest.gif

4 points for this exercise:
2 for translation and 2 for diagram.
Tell us which problem you are translating.

Hint:
It would help you to use the Set Matcher applet to check your diagram against your statement.
Compare the applet results to your alphasets example.
Do the letters in the Set Matcher match your alphaset diagram?

 

  1. I want any kind of pizza except an anchovy pizza.
  2. I want a beef pizza without anchovies.
  3. I want a pizza without anchovies and without beef.
  4. I want a beef pizza and anything but anchovies.
  5. I want either a pizza without anchovies or a pizza without beef.
  6. I want any kind of pizza but an anchovy pizza or a beef pizza.
  7. I want any kind of pizza except one that has both anchovies and beef on it.
  8. I want chicken without beef or beef without chicken.
  9. I want chicken without either anchovies or beef.
  10. I want a chicken pizza without anchovies, or I want a beef pizza.
  11. I want a chicken pizza with no anchovies and no beef.
  12. I want either a beef pizza or one that has both anchovies and chicken on it.
  13. I want a beef pizza with either anchovies or chicken.
  14. I want either both anchovies and beef or both chicken and beef.
  15. I want either beef or anchovies with either beef or chicken.
  16. I want a pizza with everything on it.
  17. I want either a pizza with beef or chicken, but not both.
  18. I don't want anchovies, don't want beef, and I don't want chicken.
  19. I want a plain pizza with nothing on it.
  20. I want any pizza except one with anchovies, beef, and chicken all mixed together. Yuck!
  21. I want a pizza with anchovies and beef or anchovies and chicken.
  22. I want a pizza with anchovies and beef or just beef alone is OK.
  23. I want a pizza with anchovies and beef or neither anchovies nor beef.
  24. I want a pizza with anchovies and beef, but without chicken.
  25. I want a pizza with anchovies and beef, or one with no beef at all.
  26. I want a pizza with anchovies and either beef or chicken.
  27. I want a pizza with anchovies and no beef and no chicken.
  28. I want a pizza with anchovies and no beef or no chicken.
  29. I want a pizza with anchovies but no chicken, or beef without chicken.
  30. I want a pizza with anchovies or beef and anchovies or chicken.
  31. I want a pizza with anchovies or beef and chicken.
  32. I want a pizza with anchovies or beef but not both.
  33. I want a pizza with anchovies or beef or chicken.
  34. I want a pizza with anchovies or beef without both anchovies and beef.
  35. I want a pizza with anchovies or beef without chicken and beef.
  36. I want a pizza with anchovies or beef without chicken.
  37. I want a pizza with anchovies or both anchovies and beef.
  38. I want a pizza with anchovies or no beef and beef or no anchovies.
  39. I want a pizza with anchovies or no beef without chicken.
  40. I want a pizza with anchovies without beef and beef without anchovies.
  41. I want a pizza with anchovies without beef or beef without anchovies.
  42. I want a pizza with anchovies without beef or chicken.
  43. I want a pizza with beef and no anchovies without chicken.
  44. I want a pizza with beef and no chicken and beef with anchovies.
  45. I want a pizza with beef or chicken and chicken or beef.
  46. I want a pizza with beef or no beef.
  47. I want a pizza with beef or no chicken and beef with anchovies.
  48. I want a pizza with beef or no chicken.
  49. I want a pizza with beef without chicken and no beef without anchovies.
  50. I want a pizza with beef without no anchovies and chicken.
  51. I want a pizza with beef.
  52. I want a pizza with chicken and beef and no anchovies.
  53. I want a pizza with chicken and beef or beef with no anchovies.
  54. I want a pizza with chicken but no beef or anchovies.
  55. I want a pizza with chicken or beef without anchovies.
  56. I want a pizza with chicken without beef.
  57. I want a pizza with chicken, or anything without beef and chicken.
  58. I want a pizza with either anchovies or chicken but without anchovies and beef.
  59. I want a pizza with no anchovies and beef or no anchovies or beef.
  60. I want a pizza with no anchovies and beef.
  61. I want a pizza with no anchovies and chicken, or beef and chicken.
  62. I want a pizza with no anchovies or beef or chicken.
  63. I want a pizza with no anchovies or beef.
  64. I want a pizza with no anchovies or no beef and no beef or no chicken.
  65. I want a pizza with no anchovies or no beef or no chicken.
  66. I want a pizza with no anchovies or no beef without chicken.
  67. I want a pizza with no anchovies or no beef.
  68. I want a pizza with no anchovies or no chicken, and no beef or no anchovies.
  69. I want a pizza with no anchovies without beef or no chicken.
  70. I want a pizza with no anchovies without beef.
  71. I want a pizza with no anchovies without chicken or no beef without chicken.
  72. I want a pizza with no anchovies, and chicken without beef.
  73. I want a pizza with no anchovies, no beef, and no chicken.
  74. I want a pizza with no anchovies.
  75. I want a pizza with no beef and chicken and anchovies.
  76. I want a pizza with no beef and chicken.
  77. I want a pizza with no beef or no chicken without beef.
  78. I want a pizza with no beef or no chicken.
  79. I want a pizza with no beef without chicken and beef and chicken.
  80. I want a pizza with no beef without chicken and beef without anchovies.
  81. I want a pizza with no beef without chicken or no anchovies without beef.
  82. I want a pizza with no beef without chicken or no beef without anchovies.
  83. I want a pizza with no chicken and beef or anchovies.
  84. I want a pizza with no chicken and no beef or chicken.
  85. I want a pizza with no chicken without beef or no beef without chicken.
  86. I want a pizza with nothing on it.
  87. I want a pizza without chicken and beef.
  88. I want a pizza without chicken.


As before, first come, first served.
If someone has already taken your order
(i.e. completed your exercise),
you must do another that no one has yet placed on the wiki.
So you may want to check the wiki first before you begin.

As in the previous exercise, the most common error is the confusion of AND with OR.
When we say AND, we mean both only.
When we say OR, we mean either or both;
we are giving the cook a choice (sometimes).
Also, make judicious use of parentheses ( ) to avoid ambiguity.
So observe your neighbor's work, as well as your own,
and correct them if in error.
There will most likely be plenty of errors.

Check the comments below as they grow with examples.
Some of the exercises refer to the same subsets.
Observe the shading of the diagrams that are correct.
See if you can tell which subsets are equal.
Identical diagrams indicate the same pizza order although the wording is different.

Click here for a Pizza Test Demo.

Comments:

From wHolt - 2/3/06 7:18 PM [Edit] [Delete]


I want anchovies and chicken without beef,
or, if it's faster, beef and chicken without anchovies,
or maybe beef and anchovies and hold the chicken.


(A&C–B) + (B&C–A) + (B&A–C)

 

Comments:

From wHolt - 12/14/06 10:34 PM

The OR in either beef or chicken is not exclusive.

From GolfGirl - 12/14/06 6:51 PM

#26 I want a pizza with anchovies and either beef or chicken

(A)&(B+C)

From Spartan - 12/14/06 7:26 AM

#46  I want a pizza with beef or no beef.

(+B) or  (-B)

From wHolt - 12/13/06 11:14 AM

Lexiowen - your notation ~(A&B)+~(A+B) does not equal a chicken pizza.
Shade every area that is not A and B.
Then shade every area that is not A or B.

From Lexiowen - 12/12/06 7:05 PM

pizza test

59. I want a pizza with no anchovies and beef or no anchovies or beef.

~(A&B)+~(A+B)

 

From wHolt - 12/12/06 11:53 AM

GolfGirl-
first add B+C
then shade that part of A inside B+C

From GolfGirl - 12/11/06 8:30 PM

I hope this is right! if it isnt am I close?

From wHolt - 12/8/06 11:18 AM

Lexiowen- not (A and B) includes many areas you did not shade. Try again.
Also copy the problem statement to your comment.

From Lexiowen - 12/7/06 10:14 PM

pizza test

59.

-(A&B)+ -(A+B)

From Fro - 10/17/06 6:57 PM

A + B + C

# 33 I want a pizza with anchovies or beef or chicken

From wHolt - 10/17/06 2:19 PM

You did not add, you intersected.

From Fro - 10/16/06 8:41 PM

A + B + C

# 33 I want a pizza with anchovies or beef or chicken

From wHolt - 10/16/06 2:35 PM

Fro - the + sign means to add all the areas together.

From Fro - 10/15/06 7:48 PM

A + B + C

# 33 I want a pizza with anchovies or beef or chicken

From DirtyBird - 10/15/06 3:19 PM

Thank You

 

From wHolt - 10/15/06 1:59 PM

DirtyBird - you got it!

From DirtyBird - 10/15/06 10:35 AM

#25) I want a pizza with anchovies and beef, or one with no beef at all.

From wHolt - 10/13/06 3:00 PM

No beef includes plain.

From wHolt - 10/12/06 7:41 PM

DirtyBird - you have yet to shade A&B. Why?

Taz - you forgot plain pizza

From Taz - 10/11/06 5:07 PM

76. I want pizza with no anchovies.

From Pac - 10/4/06 5:10 PM

Another shot!

#14: I want a pizza with either anchovies and beef or beef and chicken!

(A AND B) OR (B AND C)

From wHolt - 10/4/06 11:55 AM

Draco- you notated this: I want either beef or anchovies, with either beef or chicken.
but you shaded this: I want either beef, or anchovies with either beef or chicken.
I will take either, but be consistent.

Others who have not yet made the list should continue to work from inside the () outward.

From Draco - 10/4/06 11:28 AM

15. I want either beef or anchovies with either beef or chicken.  (B + A) & (B+C)

*correction*

From Capricorn - 10/3/06 10:01 PM

#52 I want a pizza with chicken and beef and no anchovies.

From Deuce - 10/3/06 12:36 PM

I want a pizza with no chicken and no beef or chicken.

i hope this is right this problem is killing me

From Fro - 10/2/06 9:08 PM

A + B + C

# 33 I want a pizza with anchovies or beef or chicken

From Pac - 10/2/06 7:58 PM

Fixed (I hope)!

#14: I want a pizza with either anchovies and beef or beef and chicken.

(A&B)+(B&C) = (anchovies AND beef) OR (beef AND chicken)

From Brick - 10/2/06 2:34 PM

Yes, the statements are different.  I think I did "I want a pizza with no beef and no chicken."

From wHolt - 10/2/06 1:49 PM

THIS PAGE IS NOW CLOSED TO NEW APPLICATIONS !!!



WAITERS WHO STILL WISH TO BE CONSIDERED,
MAY FIX THEIR FORMS AND RECOMMENT

From wHolt - 10/2/06 1:46 PM

NEW EMPLOYEES OF THE LOOLOOLO PIZZA PARLOR! 

7Iron
Aeneid
BassLady
Bob
Boki
Bravo
Bubba
Capricorn
CatsEyes
Centerfield
Cheana
David
Draco
Harkar
Hotrod
Houdini
JooJoo
Kathi
Melewen
Pac
Phoenix
Pod
Poovey
Pringle
RockClimber
SkoolGirl
Slick
Soller
Sunshine
SuperDuke
TBird
Tiger
Trixie
Zonino

Study the examples of those listed above.
They received full credit.
If you are not on the list, you did not complete your order.
Redo it!

When you submit an example that matches your order
with its proper notation and diagram,
you too will join the ranks of the Looloolo Pizza Parlor waiters!

From wHolt - 10/2/06 1:45 PM

Dirtybird, Fro, Draco, Deuce, GolfGirl - notation good - shading bad. FIX IT...

Bubba - fix your typo

Brick - are these statements different?
I want a pizza with no beef and chicken.
I want a pizza with no beef and no chicken.
I want a pizza with no beef or chicken.
If so, which one did you do?

Draco- #11 does say NO anchovies

From Brick - 10/2/06 12:38 AM

76. I want a pizza with no beef and chicken.

Pizza test

From SunSport - 10/1/06 9:29 PM

 #55 
  1. I want a pizza with chicken or beef without anchovies. 

From SkoolGirl - 10/1/06 9:07 PM

Pizza Test

#73 I want a pizza with no anchovies, no beef, and no chicken.

From TBird - 10/1/06 9:06 PM

3

#3 I want a pizza without anchovies and without beef.

 

From GolfGirl - 10/1/06 8:51 PM

(A)&(B+C)

#26 I want a pizza with anchovies and either beef or chicken.

From Deuce - 10/1/06 8:29 PM

I want a pizza with no chicken and no beef or chicken.

i hope this is right this problem is killing me

From Bubba - 10/1/06 8:23 PM

pizza test

#88     I want a pizza without chicken. (-A)

 

From Draco - 10/1/06 6:24 PM

15. I want either beef or anchovies with either beef or chicken.  (B + A) & (B+C)

From Fro - 10/1/06 4:30 PM

A + B + C

# 33 I want a pizza with anchovies or beef or chicken

From Poovey - 10/1/06 3:02 PM

#44 I want a pizza with beef and no chicken and beef with anchovies

(B-C) & A

??????

From wHolt - 10/1/06 2:16 PM

DirtyBird - anchovices and beef is not A+B

Poovey  - why are you using a +. There is no OR in your statement.

From Poovey - 10/1/06 12:09 PM

#44 I want a pizza with beef and no chicken and beef with anchovies

(B-C) + A

correction "take 3"  :)

From wHolt - 9/30/06 1:36 PM

RockClimber-
no chicken without beef or no beef without chicken
means you cannot have chicken without the beef
or
you cannot have beef without the chicken.
You can either interpret this as the areas where beef and chicken overlap,
or any kind of pizza except  chicken without beef or beef without chicken-
this would include anchovies alone or plain as well.

However, your last one looks good.

From RockClimber - 9/30/06 12:29 AM

#51) I want a pizza with beef.

Since you stated if the problem does not contain chicken or anchovies, exclude them all together, I translate this as I want a beef pizza.

From RockClimber - 9/29/06 12:52 AM

#85) I want a pizza with no chicken without beef or no beef without chicken. So my translation is they want a pizza with anchovies, and sauce.

From wHolt - 9/29/06 12:48 AM

RockClimber- does no chicken without beef or no beef without chicken
exclude chicken pizzas without beef or beef pizzas without chicken?
What is being excluded? and included?


Those of you who did not make the list yet, you are still confusing & with +.
It seems to be a difficulty that is built into our brains over many years of saying AND when we mean PLUS.
Remember in your CSG exersise, the & meant intersection.
In logic, BOTH means AND, not PLUS.
Also WITH means AND.
Keep at it. If you have started, you can keep trying... 

If your exercise does not mention Chicken,
then ignore the Chicken circle altogether!
Pretend it is not there.
Likewise, for Beef and Anchovy.
That may help some of you.

From Tiger - 9/28/06 6:28 PM

I want a pizza with anchovies and beef or anchovies and chicken.

From Poovey - 9/28/06 5:58 PM

#44 I want a pizza with beef and no chicken and beef with anchovies

(B-C) & (B +A)

correction "take 2"

From wHolt - 9/28/06 12:30 PM

Poovey - what does WITH mean? Does it mean OR or AND?

Everyone - Compare the examples by Bravo and Soller.
They both cannot be right.
One point extra credit to the first one who tells us why
and what the wrong one should look like!

From David - 9/28/06 10:14 AM

18.  I dont want anchovies, don't want beef, and I don't want chicken.

From Soller - 9/27/06 11:39 PM

I want a pizza with chicken but no beef or anchovies.

From Pringle - 9/27/06 6:35 PM

 #5  I want either a pizza without anchovies or a pizza without beef

From CenterField - 9/27/06 6:00 PM

Pizza Test Attempt #2

From Pac - 9/27/06 4:12 PM

14. I want either both anchovies and beef or both chicken and beef.

(A&B) + (B&C) = (anchovies and beef) OR (beef and chicken)

From wHolt - 9/27/06 12:32 AM

BassLady-your notation could be simpler.
Those of you not on today's list, are still confusing + and &.
Obviously , there is no reason to try the next assignment
till you get past this one.

From Spartan - 9/27/06 12:04 AM

13. I want a beef pizza with either anchovies or chicken.

(B+A) + (B+C)

From Bob - 9/26/06 10:33 PM

#17 I want either a pizza with beef or chicken, but not both. Hope this makes sense. 

From Pringle - 9/26/06 9:25 PM

 I want either a pizza without anchovies or a pizza without beef.

From BassLady - 9/26/06 6:27 PM

#9

I want chicken without either anchovies or beef. (A + B + C) - (A + B)

From Poovey - 9/26/06 4:28 PM

#44 I want a pizza with beef and no chicken and beef with anchovies

(B-C) & (B +A)

From wHolt - 9/26/06 1:44 PM

DirtyBird- you did not do #88

From Boki - 9/26/06 11:16 AM

I want a pizza with chicken and beef and no anchovies.
(C & B) & (-A)

From Phoenix - 9/25/06 11:45 PM

pizza test

~A

74. I want a pizza with no anchovies.

From wHolt - 9/25/06 12:37 PM

Slick interpreted #87 as I want a pizza without Beef and without Chicken.
In English, we could have interpreted it to say I want a pizza without (Beef & Chicken).
They are different.
Looloolo logic can get very picky.

Some of you may be shading correctly, but your notation is off; or vice versa.

From Slick - 9/24/06 7:50 PM

Pizzatest 3

#87 I want a pizza without Beef and Chicken

From Shanja - 9/24/06 7:08 PM

#32 I want a pizza with Anchovies or beef but not both.

From HotrodMinivan - 9/24/06 5:08 PM

Pizza test take 2

#29 I want an anchovie pizza with no chicken or a beef pizza without chicken

From Bravo - 9/24/06 4:45 PM

#11 I want a chicken pizza with out Beef and Anchovies

C (-B) (-A)

From Harkar - 9/24/06 2:27 PM

pizza test

#10 I want a chicken pizza without anchovies, or I want a beef pizza.

From Aeneid - 9/24/06 1:23 PM

B(-A)

Problem #2   B(-A)  I want a beef pizza without anchovies.

This should be a true representation

 

From Houdini - 9/23/06 7:19 PM

Negative, I guess I just over thunk the problem, (c-b)+(b-c) accomplishes the samething as my other one.

Aeneid, your order doesn't ask for a plain pizza, don't include the outside box when highlighting.

From Aeneid - 9/23/06 4:53 PM

B(-A)

#2  I want a beef pizza without anchovies

help someone if this isn't correct

From Cheana - 9/23/06 4:01 PM

#1 I want any kind of pizza except an anchovy pizza

                                                  ~A

From wHolt - 9/23/06 12:42 PM

Houdini- your notation is correct but do you need the first two terms?

From wHolt - 9/23/06 12:41 PM

Is there a difference between
A pizza without beef AND chicken
and
A pizza without beef OR chicken ?

From Slick - 9/23/06 10:37 AM

Pizzatest Rev

#87 I want a pizza without chicken and beef.

From Trixie - 9/22/06 10:19 PM

pizza test

I want a plain pizza with nothing on it.

From Houdini - 9/22/06 9:23 PM

#8 I wan't chicken without beef or beef without chicken. 

Third times the charm!

If this isn't right then someone please help me.

From wHolt - 9/22/06 12:39 PM

Houdini - you will get it next time...

From Houdini - 9/21/06 10:22 PM

I want chicken without beef or beef without chicken. 

Please, please, please be right.

From CatsEyes - 9/21/06 7:57 PM

#86 - I want a pizza with nothing on it.

From 7Iron - 9/21/06 11:14 AM

PizzaTest
7. I want anykind of pizzaexcept one that has both anchovies and beef on it.

From Pod - 9/20/06 9:17 PM

I noticed, in addition to doing the problem wrong, I skipped one of the main instructions - do 1-20 first, then choose from others.  So, have chosen instead to do #6.

 6 - I want any kind of pizza but an anchovy pizza or a beef pizza.

From HotrodMinivan - 9/20/06 4:39 PM

Pizza Test #29

#29 (a-c) + (b-c)  I want a pizza with anchovies with no chicken or beef without chicken

The notation in the applet is wrong, I corrected it here.

From Sunshine - 9/20/06 2:06 PM

Anchovies no chicken no beef

From wHolt - 9/20/06 12:28 AM

I WILL NOT BE GIVING YOU ANY MORE FEEDBACK ON THESE SUBMISSIONS
UNLESS YOU MATCHED YOUR DIAGRAM AND NOTATION WITH YOUR ORDER.

IF YOU DO NOT MATCH THE ORDER GIVEN, REDO IT.
WHEN YOU REDO, DO NOT EDIT YOUR COMMENT;
MAKE A NEW COMMENT AND DELETE YOUR OLD ONE.
OR IT WILL NOT BE SEEN AND SCORED.

OF COURSE,
YOU MAY RECEIVE HELP FROM OTHERS BECAUSE THE ASSIGNMENT IS PUBLIC.
MOST OF YOUR ERRORS WILL BE BECAUSE YOU CONFUSE + AND &.
Don't subtract from a circle unless the notation says to!
YOUR OTHER ERRORS WILL COME FROM INCORRECT SHADING.

From Houdini - 9/19/06 9:53 PM

#8 I want chicken without beef or beef without chicken.

From Butterfly - 9/19/06 7:15 PM

I want a beef pizza and anything but Anchovies.

From wHolt - 9/19/06 11:54 AM

DirtyBird- does your order exclude plain pizza?
did you confuse AND with OR ?

Slick - does your order not include plain pizza?
is "I want a pizza without chicken and beef"
the same as "I want a pizza without chicken OR beef"?

TBird- does your order allow Chicken with anchovies and beef?

From Slick - 9/18/06 7:07 PM

     #87  I want a pizza without chicken and beef.

Pizzatest

From Melewen - 9/18/06 3:59 PM

Pizza order

24. I want a pizza with anchovies and beef, but no chicken.  

From wHolt - 9/18/06 11:41 AM

TBird - your order said nothing about chicken. Redo

Pod - your order did not say to remove anchovies from the chicken. Redo.

From Pod - 9/18/06 10:33 AM

56. I want a pizza with chicken without beef.

C(-B)

From SuperDuke - 9/18/06 10:19 AM

JooJoo,

I believe you should have an operator ( + , - , or & ) in between the "C" and ther parenthesis.

I also believe you should have an operator between the two sets of Parenthesis.

From Kathi - 9/18/06 5:23 AM

I want any kind of pizza except anchovy 

From SuperDuke - 9/17/06 11:53 PM

#20

#20-  I want any pizza except one with anchovies, beef, and chicken all mixed together. Yuck!

From JooJoo - 9/17/06 9:13 PM

pizza test

 

#11. I want a chicken pizza with no anchovies and no beef, C(-A)(-B)

From wHolt - 9/17/06 1:33 PM

Aeneid- you also subtracted C. Don't.
Thanks, Zonino.

Everyone - Make sure to copy your statement like Zonino did.

From Zonino - 9/17/06 12:20 AM

#16 - I want a pizza with everything on it.  (A AND B AND C)

From Aeneid - 9/17/06 12:15 AM

B(-A)

#2 I want a beef pizza without anchovies


Last Modified 9/16/06 9:40 PM

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