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Thread: Find n(P∩Q∩R')

  1. #1
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    Find n(P∩Q∩R')

    Hello, last question for tonight but I was doing a venn diagram question and I made it all the way to the almost end, there's just one last part that is getting me.

    The question states that given three sets, P,Q, and R such that R is a subset of Q and n(U) =(P∪Q∪R)=100, n(Q∪R)=75, n(Q ∩ R) = 41, n(p ∩ R)=15,
    n(P)=44 and n(Q')= 25.

    They asked to draw a venn diagram representing this information which I will post a picture of.

    AS you can see I calculated all the values carefully, now the question finally asks, ''Hence determine n[(P∩Q)∩R')''.

    This is where I stick up, I'm thinking things like, ok to find the intersection of P and Q because that is what they're asking for, I should first find the union, but the problem with that is using the formula to find the union of two sets, I need the intersection!

    So I just can't figure it out for the life of me, it's the area on the photo with the ''?''ji.jpg

  2. #2
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    Quote Originally Posted by richiesmasher View Post
    Hello, last question for tonight but I was doing a venn diagram question and I made it all the way to the almost end, there's just one last part that is getting me.

    The question states that given three sets, P,Q, and R such that R is a subset of Q and n(U) =(P∪Q∪R)=100, n(Q∪R)=75, n(Q ∩ R) = 41, n(p ∩ R)=15,
    n(P)=44 and n(Q')= 25.

    They asked to draw a venn diagram representing this information which I will post a picture of.

    AS you can see I calculated all the values carefully, now the question finally asks, ''Hence determine n[(P∩Q)∩R')''.

    This is where I stick up, I'm thinking things like, ok to find the intersection of P and Q because that is what they're asking for, I should first find the union, but the problem with that is using the formula to find the union of two sets, I need the intersection!

    So I just can't figure it out for the life of me, it's the area on the photo with the ''?''ji.jpg
    How did you find each number? The way I did it, I found the "?" before I found the 30.

    P consists of three regions; you know the total and two parts, so you can find the third. I don't see a need to find P∩Q first.

  3. #3
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    Quote Originally Posted by Dr.Peterson View Post
    How did you find each number? The way I did it, I found the "?" before I found the 30.

    P consists of three regions; you know the total and two parts, so you can find the third. I don't see a need to find P∩Q first.
    For R∩P that was given as 15.
    so for the Second region of R I just did 41 -15 = 26

    For the region marked 30, which is just Q by without any intersections or unions, I did this: P∪R = 44+41-15= 70, so then I knew that if the total is 100, then Q must be equal to 100-70=30.

    For the region marked 25, which is Q', I simply used the fact that Q is 75 and subtracted from 100, and there you go.

    And I was stuck but I see what you mean about regions, I guess I wasn't recognizing them, the answer was right in front of my face it would just be 44-40=4.

  4. #4
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    Quote Originally Posted by richiesmasher View Post
    For R∩P that was given as 15.
    so for the Second region of R I just did 41 -15 = 26

    For the region marked 30, which is just Q by without any intersections or unions, I did this: P∪R = 44+41-15= 70, so then I knew that if the total is 100, then Q must be equal to 100-70=30.

    For the region marked 25, which is Q', I simply used the fact that Q is 75 and subtracted from 100, and there you go.

    And I was stuck but I see what you mean about regions, I guess I wasn't recognizing them, the answer was right in front of my face it would just be 44-40=4.
    I see what you did for the 30; I just didn't happen to see that before I saw the 4. But you've got it all now.

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