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August 31st, 2010, 09:54 AM   #1
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I need help with these question on Sets...

Hi,

I am currently revising for a Math test with a past exam paper. I'm stuck on question on Sets. I've answered some of them. I was wondering if some can help me work it out.

Two sets are defined as follows:

A = {n ? ? : ?m ? ? 3m = n}
B = {n ? ? : 5 ? n ? 7}

1. Describe, in words, the elements of A.

For this I wrote: It is a set of natural numbers. It contains an existential quantification, which has to be a integer of 3 that will equal n.

^^^Am I right with my explanation? If I'm wrong can I get the proper definition of it?

2. Write out explicitly (by listing the elements).
a) B = {5,6,7}
b) B - A = {2,3,4}
c) B ? A =
d) B x B =
e) ?B =
f) where the universal set is {1,2,3,4,5,6,7}
=

I could only answer two of these. Is is possible some can help me work this out and give me an explanation on how it was worked out?

And if it isn't to much hassle can someone make up additional questions so I can go work it on my own, using the explanations that's been given?
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August 31st, 2010, 11:22 AM   #2
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Re: I need help with these question on Sets...

Quote:
Originally Posted by Britmouth
1. Describe, in words, the elements of A.

For this I wrote: It is a set of natural numbers. It contains an existential quantification, which has to be a integer of 3 that will equal n.
"Positive multiples of 3" would have been my answer.
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August 31st, 2010, 11:48 AM   #3
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Re: I need help with these question on Sets...

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by Britmouth
1. Describe, in words, the elements of A.

For this I wrote: It is a set of natural numbers. It contains an existential quantification, which has to be a integer of 3 that will equal n.
"Positive multiples of 3" would have been my answer.
So is what I wrote is right, but just long winded?
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August 31st, 2010, 12:11 PM   #4
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Re: I need help with these question on Sets...

Quote:
Originally Posted by Britmouth
So is what I wrote is right, but just long winded?
I don't know. It looks like you transliterated the math rather than understood it and rewrote it. It's possible that the teacher would have given credit.
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August 31st, 2010, 02:43 PM   #5
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Re: I need help with these question on Sets...

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by Britmouth
So is what I wrote is right, but just long winded?
I don't know. It looks like you transliterated the math rather than understood it and rewrote it. It's possible that the teacher would have given credit.
Ok, thanks. I've worked out a couple more of the questions...

2. Write out explicitly (by listing the elements).
a) B = {5,6,7}
b) B - A = {5,6,7}
c) B ? A = {3,6}
d) B x B = {(5,5),(5,6),(5,7),(6,5),(6,6),(6,7),(7,5),(7,6),( 7,7)}
e) ?B = {,{5},{6},{7},{5,6},{5,7},{6,7},{5,6,7}}
f) where the universal set is {1,2,3,4,5,6,7} =

Can someone check if i'm correct with these? Any=d any help on the last part?
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August 31st, 2010, 05:58 PM   #6
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Re: I need help with these question on Sets...

Quote:
Originally Posted by Britmouth
2. Write out explicitly (by listing the elements).
a) B = {5,6,7}
b) B - A = {5,6,7}
c) B ? A = {3,6}
d) B x B = {(5,5),(5,6),(5,7),(6,5),(6,6),(6,7),(7,5),(7,6),( 7,7)}
e) ?B = {,{5},{6},{7},{5,6},{5,7},{6,7},{5,6,7}}
f) where the universal set is {1,2,3,4,5,6,7} =

Can someone check if i'm correct with these? Any=d any help on the last part?
Right: a, d, e
Wrong: b, c

f is the same as asking for {1,2,3,4,5,6,7} - B.
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August 31st, 2010, 06:08 PM   #7
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Re: I need help with these question on Sets...

For b), one of {5,6,7} is in A, so you would have to exclude that element from your answer. The set difference B - A cannot contain any elements in common with A.
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