Question 184847: Please help me with the following question. Ireally need the help my work is due today and I just don't get it.
1.Set K contains 30 elements, set J contains 46 elements, and 11 elements are common to both sets. Find n ( K U J).
2.Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A ∩ C
c) A U C
d) B U C
e) (A U B) ∩ C
f) A U (B U C)
g) (A ∩ B) ∩ C
h) (A ∩ B) U C
Please help me
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
To find the number of elements in the set K U J, simply add the two sets together. However, remember to subtract the number of elements in both sets (since these elements are repeated)
In other words, use this formula:
n ( K U J) = n(K) + n(J) - n(K ∩ J)
In this case, n(K)=30, n(J)=46 and n(K ∩ J) = 11. Plug these values in to get:
n ( K U J) = 30 + 46 - 11
Add
n ( K U J) = 76 - 11
Subtract
n ( K U J) = 65
So there are 65 elements in set K U J
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# 2
I'll do the first four to get you started
a)
A ∩ B = Set of elements that BOTH sets A and B have in common
A ∩ B = {1, 2, 3} ∩ {3, 4, 5, 6}
A ∩ B = {3}
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b)
A ∩ C = Set of elements that BOTH sets A and C have in common
A ∩ C = {1, 2, 3} ∩ {3, 5, 7}
A ∩ C = {3}
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c)
A U C = Combination of the sets A and C (remove any duplicates)
A U C = {1, 2, 3} U {3, 5, 7}
A U C = {1,2,3,5,7}
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d)
B U C = Combination of the sets B and C (remove any duplicates)
B U C = {3, 4, 5, 6} U {3, 5, 7}
B U C = {3,4,5,6,7}
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