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Difficulty: 3 of 5 Latest: Set Theory (in General)

  
The following is a list of 15 thought provoking statements
about sets where a true or false answer is needed.
A denotes any set, F the set {1,2}, φ the empty set,
and ℘(S) the set of all subsets of set S (i.e, the power
set of S).

a)   φ∩{φ} = {φ}
b)   φ∪{φ} = {φ,{φ}}
c)   φ ∈ ℘({φ,{φ}})
d)   {φ} ⊆ A
e)   φ ⊆ A
f)   φ ⊆ ℘(A)
g)   {{φ}} ⊆ ℘(φ)
h)   {φ}∩φ = φ
i)   ℘(φ) = {φ,{φ}}
j)   φ ∈ A
k)   φ ∈ ℘(A)
l)   {φ} ∈ ℘(A)
m)   {φ}∪φ = {φ}
n)   φ ⊆ ℘(F)-φ
o)   {φ} ⊆ {{φ,{φ},{{φ}}}}

From "Bridge to Abstract Mathematics",1987
          by Ronald P. Morash.
  
(No Solution Yet, 3 Comments) Submitted on 2014-04-19 by Bractals   
Difficulty: 3 of 5 Bonus: The Tunnel (in Logic) Rating: 3.54
You have entered a mysterious tunnel with your friend. As you get to the middle of the room, flames rise at both ends, disallowing you from exiting.

On a table you see a row of 7 bottles of potions, each a different size. The largest bottle is second from the left, and the smallest is fourth from the right. There also is a riddle.

"Danger lies before you, while safety lies behind,
Two of us will help you, whichever you would find.
One among us seven will let you move ahead,
another will transport the drinker back instead,
Two among our number hold only nettle wine,
Three of us are killers, waiting hidden in line.
Choose, unless you wish to stay here forevermore,
To help you in your choice, we give you these clues four
First, however slyly the poison tries to hide
You will always find some on nettle wine's left side;
Second, different are those who stand at either end.
But if you would move onward, neither is your friend;
Third as you see clearly, all are different size.
Neither dwarf nor giant holds death in their insides;
Fourth, the second left and the second on the right
Are twins once you taste them, though different at first sight.

Which bottle will contain the potion to allow you to continue on in the tunnel, and which one will allow your friend to go backward in the tunnel?

(Taken from "Harry Potter and the Sorcerer's Stone")
(Solution Posted, 16 Comments) Submitted on 2003-12-16 by Gamer   
Difficulty: 3 of 5Mean Muse (in Just Math)
Posted on 2014-04-18 by K Sengupta (No Solution Yet, 0 Comments)
Difficulty: 2 of 5Neighbors (in Numbers)
Posted on 2014-04-18 by Ady TZIDON (No Solution Yet, 8 Comments)
Difficulty: 4 of 5No way to win (in General)
Posted on 2014-04-17 by Ady TZIDON (No Solution Yet, 4 Comments)
Difficulty: 2 of 5Murderer Detection (in Riddles) Rating: 3.00
Posted on 2014-04-17 by K Sengupta (No Solution Yet, 2 Comments)
Difficulty: 3 of 5Cubic Sequence? (in Sequences)
Posted on 2014-04-16 by K Sengupta (No Solution Yet, 2 Comments)
Difficulty: 2 of 5Colorful hats (in Logic) Rating: 2.00
Posted on 2014-04-16 by Math Man (No Solution Yet, 4 Comments)
Difficulty: 3 of 5Mod 3 alphametics (in Just Math)
Posted on 2014-04-15 by Ady TZIDON (No Solution Yet, 2 Comments)
Difficulty: 2 of 5My phone is 2543663 (in Probability) Rating: 4.00
Posted on 2014-04-15 by Ady TZIDON (No Solution Yet, 5 Comments)
Difficulty: 4 of 5Pseudo-FIBO (in Sequences)
Posted on 2014-04-14 by Ady TZIDON (No Solution Yet, 5 Comments)
Difficulty: 3 of 5Question Quandary (in Logic) Rating: 3.00
Posted on 2014-04-14 by K Sengupta (No Solution Yet, 2 Comments)
Difficulty: 4 of 5The right subset (in Word Problems)
Posted on 2014-04-13 by Ady TZIDON (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Geometric Sequence Settlement II (in Just Math) Rating: 3.00
Posted on 2014-04-12 by K Sengupta (No Solution Yet, 1 Comments)
Difficulty: 3 of 5Upside down (OEIS A045573) (in Numbers)
Posted on 2014-04-11 by Ady TZIDON (No Solution Yet, 6 Comments)
Difficulty: 3 of 5Synonym Set (in Word Problems)
Posted on 2014-04-11 by K Sengupta (No Solution Yet, 1 Comments)

Recently Posted Solutions:
Difficulty: 3 of 5Q: What is this sum? (in Numbers)
Submitted By Ady TZIDON. Solution posted on 2014-04-09 00:05:29
Difficulty: 4 of 5It is not that easy (in General)
Submitted By Ady TZIDON. Solution posted on 2014-04-08 23:53:41
Difficulty: 3 of 5Logical connectives (in Algorithms)
Submitted By Math Man. Solution posted on 2014-04-03 18:51:23
Difficulty: 3 of 52 to 1 Bisector (in Geometry)
Submitted By Bractals. Solution posted on 2014-04-03 16:39:37
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Submitted By tomarken. Solution posted on 2014-03-24 13:44:53
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