anonymous
  • anonymous
If U = {1,2,3,4,5,6,7,8,9, l0} and A = {1,2,3} B = {2,4,6,8} C = {7,8,9,10} Find the following: a. A′ b. (A U B) c. (A′ ∩ B)′
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnkleRhaukus
  • UnkleRhaukus
A', is the set of all element in the universal set U, but not in the set A.
UnkleRhaukus
  • UnkleRhaukus
A∪B, is the set of all elements in either A or B.
anonymous
  • anonymous
What would the answers be? Is A' = 1,2,3,4,5,6,7,8,9,10?

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More answers

UnkleRhaukus
  • UnkleRhaukus
no, 1,2,3 are in A
anonymous
  • anonymous
oh wait, it would be 4,5,6,7,8,9,10
UnkleRhaukus
  • UnkleRhaukus
that's better.
anonymous
  • anonymous
So (AUB) = 1,2,3,4,6,8?
UnkleRhaukus
  • UnkleRhaukus
yep
UnkleRhaukus
  • UnkleRhaukus
Now for the last one (A′ ∩ B), is the set all elements in both A' and B. (A′ ∩ B)′, is the set of all elements in the universal set U, but not in (A′ ∩ B).
anonymous
  • anonymous
So (A' and B') = 123?
UnkleRhaukus
  • UnkleRhaukus
find (A′ ∩ B) first
UnkleRhaukus
  • UnkleRhaukus
there should not be any `B'`
anonymous
  • anonymous
(a' union b) is {2,4,5,6,7,8,9,10)
UnkleRhaukus
  • UnkleRhaukus
\(\cap\) is the intersection, (not the union)
anonymous
  • anonymous
whats the answer for the last one?
UnkleRhaukus
  • UnkleRhaukus
(A′ ∩ B) = {4,5,6,7,8,9,10} ∩ {2,4,6,8} =
anonymous
  • anonymous
So (a' intersection b)' = 4,6,8
UnkleRhaukus
  • UnkleRhaukus
No, (A′ ∩ B) = {4,6,8} Now find (A′ ∩ B)′
anonymous
  • anonymous
how do I find that?
UnkleRhaukus
  • UnkleRhaukus
(A′ ∩ B)′ = U \ (A′ ∩ B) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \ {4, 6, 8} (where \ is setminus)
anonymous
  • anonymous
so that's that answer?
UnkleRhaukus
  • UnkleRhaukus
no, simplify
UnkleRhaukus
  • UnkleRhaukus
take the elements 4,6,8, from the universal set
anonymous
  • anonymous
then what
UnkleRhaukus
  • UnkleRhaukus
then you will have the answer to c.
anonymous
  • anonymous
so its (1,2,3,5,7,9,10) / (4,6,8)?
UnkleRhaukus
  • UnkleRhaukus
perform the setminus operation
anonymous
  • anonymous
can you just give me the answer? I don't understand.
UnkleRhaukus
  • UnkleRhaukus
for example {0, 15, 18, 100, 458} \ {18,100} = {0, 15, 458}
anonymous
  • anonymous
so its 1, 2, 3, 5, 7, 9,10?
UnkleRhaukus
  • UnkleRhaukus
that's right. but don't forget to write the braces around the elements of a set (A′ ∩ B)′ = {1, 2, 3, 5, 7, 9, 10}
anonymous
  • anonymous
thank you!

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