GC214W0 - New Math
By: Mathman, SirCumference,The Better Half, & Cutie Pi
1. Here are website links that will help you answer the questions for this puzzle:
Set Theory:https://en.wikipedia.org/wiki/Set_theorySet Theory Inventor:https://en.wikipedia.org/wiki/Georg_CantorSputnik 1:http://www.space.com/17888-first-satellite-sputnik-1-explained-infographic.html
2. Here is the puzzle:
You will need to answer some simple questions regarding the following Sets to find the FINAL cache coordinates. The Cache is at…
N 44 58.A B C , W 089 3D. E F G
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
S= {Rick Blick, Bandits, {GMO, BlackCat} }
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
S= {Rick Blick, Bandits, {GMO, BlackCat} }
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Set X = {1,2,3, {4,5} }
Set Y = {4,5}
Set Z = {1,6,7}
Set Y = {4,5}
Set Z = {1,6,7}
3. How to answer A:
A = The number of Elements in Set R
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
The Elements for R are as follows:
Element 1 is: OPS
Element 2 is: Rick Blick
Element 3 is: baileyhk
Element 4 is: {GMO,BlackCat} - (brackets signify that this group is to be treated as one Element)
Therefore:
A = The number of Elements in Set R = 4
∪ is the symbol used to signify Union, which is the combined Elements of the listed sets.
The Elements for R are:
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
Element 1 is: OPS
Element 2 is: Rick Blick
Element 3 is: baileyhk
Element 4 is: {GMO,BlackCat} - brackets signify that the group is treated as one Element
The Elements for S are:
S= {Rick Blick, Bandits, {GMO, BlackCat} }
Element 1 is: Rick Blick
Element 2 is: Bandits
Element 3 is: {GMO,BlackCat}
By combining the Elements of the two Sets we will get R ∪ S, as follows:
Element 1 is: OPS
Element 2 is: Rick Blick
Element 3 is: baileyhk
Element 4 is: {GMO,BlackCat}
Element 5 is: Bandits
Therefore:
B = The number of Elements in R ∪ S = 5
5. How to answer C:
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
S= {Rick Blick, Bandits, {GMO, BlackCat} }
The Elements that are in both Set R and Set S are as follows:
Rick Blick
{GMO,BlackCat}
Therefore, (R ∩ S) is the Set {Rick Blick, {GMO,BlackCat} }
Second, identify the elements that are in Set T
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Third, solve the expression (R ∩ S) ∪ T.
(R ∩ S) = {Rick Blick, {GMO,BlackCat} }
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Therefore, (R ∩ S) ∪ T is the set {Rick Blick, {GMO,BlackCat}, Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Fourth, list the Elements that satisfy the expression (R ∩ S) ∪ T.
Element 1 is: Rick Blick
Element 2 is: {GMO,BlackCat}
Element 3 is: Rob Greene
Element 4 is: OPS
Element 5 is: David Cantrell
Element 6 is: BirdDog
Element 7 is: Snoopy007
Element 8 is: baileyhk
Element 9 is: Huggie Bear
Therefore:
C = The number of Elements in (R ∩ S) ∪ T = 9
6. How to answer D:
Set X = {1,2,3, {4,5} }
Set Z = {1,6,7}
7. How to answer E:
Therefore:
E = Y ∩ Y' = 0
8. How to answer F:
Read about Sputnik 1 at the following website:
http://www.space.com/17888-first-satellite-sputnik-1-explained-infographic.html
(Although you will find conflicting information at Wikipedia.com, which states that Sputnik 1 had one radio transmitter with two bandwidths, for this puzzle, the answer is 2.)
Therefore:
F = The number of radio transmitters in Sputnik 1 = 2
9. How to answer G:
0 = Cantor
1 = Bolzano
2 = Dedekind
3 = Mathman!
Read about the inventor of Set Theory at the following website:
https://en.wikipedia.org/wiki/Georg_Cantor
Therefore:
G = The person credited with Set Theory is... = 0
10. Put your solved coordinates together.
B = 5
C = 9
D = 1
E = 0
F = 2
G = 0
11. Verify the solved coordinates using GeoChecker:
4. How to answer B:
B = The number of Elements in R ∪ S
∪ is the symbol used to signify Union, which is the combined Elements of the listed sets.
In this case, all of the Elements of Sets R and S should be combined.
The Elements for R are:
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
Element 1 is: OPS
Element 2 is: Rick Blick
Element 3 is: baileyhk
Element 4 is: {GMO,BlackCat} - brackets signify that the group is treated as one Element
The Elements for S are:
S= {Rick Blick, Bandits, {GMO, BlackCat} }
Element 1 is: Rick Blick
Element 2 is: Bandits
Element 3 is: {GMO,BlackCat}
By combining the Elements of the two Sets we will get R ∪ S, as follows:
Element 1 is: OPS
Element 2 is: Rick Blick
Element 3 is: baileyhk
Element 4 is: {GMO,BlackCat}
Element 5 is: Bandits
Therefore:
B = The number of Elements in R ∪ S = 5
5. How to answer C:
C = The number of Elements in (R ∩ S) ∪ T
First, identify the elements that are in the Set (R ∩ S).
∩ is the symbol used to signify Intersection, which is the Elements that the listed Sets have in common.
In this case, we need to identify the Elements that Sets R and S have in common.
R = {OPS, Rick Blick, baileyhk, {GMO,BlackCat} }
S= {Rick Blick, Bandits, {GMO, BlackCat} }
The Elements that are in both Set R and Set S are as follows:
Rick Blick
{GMO,BlackCat}
Therefore, (R ∩ S) is the Set {Rick Blick, {GMO,BlackCat} }
Second, identify the elements that are in Set T
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Third, solve the expression (R ∩ S) ∪ T.
∪ is the symbol used to signify Union, which is the combined Elements of the listed sets.
In this case, all of the Elements of Set (R ∩ S) and Set T should be combined.
(R ∩ S) = {Rick Blick, {GMO,BlackCat} }
T= {Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Therefore, (R ∩ S) ∪ T is the set {Rick Blick, {GMO,BlackCat}, Rob Greene, OPS, David Cantrell, BirdDog, Snoopy007, baileyhk, Huggie Bear}
Fourth, list the Elements that satisfy the expression (R ∩ S) ∪ T.
Element 1 is: Rick Blick
Element 2 is: {GMO,BlackCat}
Element 3 is: Rob Greene
Element 4 is: OPS
Element 5 is: David Cantrell
Element 6 is: BirdDog
Element 7 is: Snoopy007
Element 8 is: baileyhk
Element 9 is: Huggie Bear
Therefore:
C = The number of Elements in (R ∩ S) ∪ T = 9
6. How to answer D:
D = X ∩ Z
Set X = {1,2,3, {4,5} }
Set Z = {1,6,7}
∩ is the symbol used to signify Intersection, which is the Elements that the listed Sets have in common.
In this case, we need to identify the Elements that Sets X and Z have in common.
The only Element that both Sets have in common is 1.
Therefore:
D = X ∩ Z = 1
7. How to answer E:
E = Y ∩ Y'Since there is no Set Y', there are no common Elements.
Therefore:
E = Y ∩ Y' = 0
8. How to answer F:
F = The number of radio transmitters in Sputnik 1
Read about Sputnik 1 at the following website:
http://www.space.com/17888-first-satellite-sputnik-1-explained-infographic.html
(Although you will find conflicting information at Wikipedia.com, which states that Sputnik 1 had one radio transmitter with two bandwidths, for this puzzle, the answer is 2.)
Therefore:
F = The number of radio transmitters in Sputnik 1 = 2
9. How to answer G:
G = The person credited with Set Theory is...
0 = Cantor
1 = Bolzano
2 = Dedekind
3 = Mathman!
Read about the inventor of Set Theory at the following website:
https://en.wikipedia.org/wiki/Georg_Cantor
Therefore:
G = The person credited with Set Theory is... = 0
10. Put your solved coordinates together.
N 44 58.A B C , W 089 3D. E F GA = 4
B = 5
C = 9
D = 1
E = 0
F = 2
G = 0
N 44° 58.459, W 089° 31.020
11. Verify the solved coordinates using GeoChecker:
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