Question about sets and powersets

nikosan

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Mar 12, 2016
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"Let S be the set {x : x ∈ Z and either x ≤ −2 or x ≥ 5} and let T be the set{−3, −2, −1, 4, 5, 6, 7}. Find the following."

These are what I have so far.

(i) S ∩ T = -3, -2, 5, 6, 7
(ii) S ∪ T = -3, -2, -1, 4, 5, 6, 7
(iii) S∆T = 4, -1

(iv) P(S) ∩ {{−3, −2, 1}, {4}, {6, 7}, {−5, 6, 9}}

I'm a bit confused however as to what this question is asking, so it wants the intersection between the powerset S and the subsets of T that are listed. But how do you express the powerset of S?
 
"Let S be the set {x : x ∈ Z and either x ≤ −2 or x ≥ 5} and let T be the set{−3, −2, −1, 4, 5, 6, 7}. Find the following."

These are what I have so far.

(i) S ∩ T = -3, -2, 5, 6, 7
Aren't sets supposed to be enclosed in curly braces? (I agree with the listed elements, though.)

(ii) S ∪ T = -3, -2, -1, 4, 5, 6, 7
Not even close. :shock:

Try listing out (enough to see the pattern) the elements of S. Then note that unions contain any element that is in either of the sets.

(iii) S∆T = 4, -1
What does your book mean by the "delta" operator?

(iv) P(S) ∩ {{−3, −2, 1}, {4}, {6, 7}, {−5, 6, 9}}
Does "P(X)" mean "the power set of the set X"? If so, how did you obtain this listing?

how do you express the powerset of S?
To learn what power sets are, and how to express them, please try here. (Note: The power set of S will be infinite. I'm not sure how one would "list" all of the elements...?) ;)
 
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