Math/Geometry....so confusing! Please help!

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jenzy569

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Help me please! It's so confusing :(

1. The cardinal number of the set {cat, dog, horse, fish, lizard, meerkat, rhinoceros, elephant, giraffe, platypus, hippopotamus, skunk, mouse, chipmunk, squirrel} is _________.


2. Given the following sets, select the statement below that is true.
A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t}

B ? C and C ? A
C ? B and D ? B
D ? A and A ? D
B ? A and C ? D
D ? A and A ? C


3. Without writing them all out, what is the number of subsets of set
A = {king, queen, knight, prince, princess, duke}?


4. Given the following set, select the statement below that is true.
V = {a, e, i, o, u}
s ? V
o ? V
e ? V
V intersect Ø
w ? V


5. Given these sets:
A = {3, 4, 5, 6, 7}
B = {6, 7, 8, 9}
C = {2, 4, 6, 8}

List the elements of this set
A intersect(B?C)
Do not skip to the answer. Show your work, step by step.


6. The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 23 said they had taken physics, 47 said they had taken chemistry and 5 said they had taken both. Seven said they had taken neither. How many recent high school grads were surveyed?


7. The Wildlife Federation surveyed 290 San Diego residents. The results are as follows:

44 had a membership to the Birch Aquarium
79 had a membership to the San Diego Zoo
28 had both

Construct a Venn diagram and answer the following questions:

i. How many had only a zoo membership?
ii. How many had only an aquarium membership?
iii. How many belonged to either one or the other or both?
iv. How many belonged to neither?
 
jenzy569 said:
Help me please! It's so confusing :(

1. The cardinal number of the set {cat, dog, horse, fish, lizard, meerkat, rhinoceros, elephant, giraffe, platypus, hippopotamus, skunk, mouse, chipmunk, squirrel} is _________.
Click to expand...
Most people here will not give answers. They will provide help instead.
Let's go one question at a time.
Name a few cardinal numbers.
Does your book give a process for determining the cardinal number of a set? Does your book give a definition?
If not, look at the first two sentences at http://www.daviddarling.info/encycloped ... umber.html which I found by googling "cardinal number of a set."
Now can you give me the answer to question 1? If so we can proceed to question 2.
 
So, the cardinal number for number 1 is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} right?
 
jenzy569 said:
So, the cardinal number for number 1 is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} right?
Click to expand...
Just about right. The cardinal number is a number, not a particular set. The cardinal number for your animal set is 15 as is the cardinal number of the set of numbers above. The cardinal number of any set which has 15 unduplicated elements is 15. More generally, the cardinal number of any set with n unduplicated elements is n. Now I may be being a bit over-simplistic, especially with reference to sets with cardinal numbers that are infinite, but that is the intuitive concept. Not difficult at all.

2. Given the following sets, select the statement below that is true.
A = {l, a, t, e, r}, B = {l, a, t, e}, C = {t, a, l, e}, D = {e, a, t}

B ? C and C ? A
C ? B and D ? B
D ? A and A ? D
B ? A and C ? D
D ? A and A ? C
Click to expand...
Ok, Concepts first. The order in which elements of a set are given is immaterial. The set {horse, cow) is the same as {cow, horse} is the same as {cow, horse, horse}.

There is a brief review of set concepts and set notation at http://www.purplemath.com/modules/setnotn.htm

So, the notation C ? A just means that C is a subset of A. Look at the first choice given above.
A = {l, a, t, e, r} = {a, e, l, r, t} because order is immaterial.
C = {t, a, l, e} = {a, e, l, t}.
Is every element in C an element of A? Yes.
So it is true that C ? A.

The notation B ? C means that B is a proper subset of C.
B = {l, a, t, e} = {a, e, l, t}.
Is every element in B an element of C?
Yes so B ? C.
Is there an element of C that is not an element of B?
No, so it is false that B ? C.
Therefore the first statement above is false.

Can you now work through the rest of the choices in question 2?

Something wierd is happening. My edits are not coming through. I have tried four times to refer to http://en.wikipedia.org/wiki/Subset, which indicates that there is not uniform agreement on notation for proper subsets.
 


We received your order for eleven items.

Would you like fries with that?

The post titled "Read Before Posting" provides guidelines on how to properly ask for help on these boards. Cheers 8-)

 
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