Question 1008189: Let the universal set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, and the following
subsets of A :
B is the set of elements of A multiple of 2 and less than 11.
C is the set of elements of A that are odd and less than 10.
D is the set {0, 1, 10, 11}.
Determine the cardinality of the following sets. You are not obliged to justify
your answer, but explanations can earn you partial points in case of wrong answer.
a) C ∪ D :
b) B ∪ C ∪ D :
c) (B \ C) ∪ (C \ B) :
d) (B ∩ D) ∪ C :
e) (B ∩ C) :
f) B \ D :
g) B ∪ C :
h) B ∩ C ∩ D :
i) (B ∪ C) ∩ D :
j) D \ (B ∪ C) :
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first five parts (a through e) to get you started
Given Sets:
A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
B = {0,2,4,6,8,10}
C = {1,3,5,7,9}
D = {0, 1, 10, 11}
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a)
C U D = {1,3,5,7,9} U {0, 1, 10, 11}
C U D = {1,3,5,7,9, 0, 1, 10, 11}
C U D = {0,1,3,5,7,9,10,11}
The cardinality is 8.
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b)
B = {0,2,4,6,8,10}
C = {1,3,5,7,9}
D = {0, 1, 10, 11}
B U C U D = {0,2,4,6,8,10} U {1,3,5,7,9} U {0, 1, 10, 11}
B U C U D = {0,2,4,6,8,10, 1,3,5,7,9} U {0, 1, 10, 11}
B U C U D = {0,1,2,3,4,5,6,7,8,9,10} U {0, 1, 10, 11}
B U C U D = {0,1,2,3,4,5,6,7,8,9,10, 0, 1, 10, 11}
B U C U D = {0,1,2,3,4,5,6,7,8,9,10,11}
There are 12 items in the set. The cardinality of B U C U D is 12.
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c)
B = {0,2,4,6,8,10}
C = {1,3,5,7,9}
B \ C = {0,2,4,6,8,10}
C \ B = {1,3,5,7,9}
Note: B and C are mutually exclusive sets, so there's nothing to kick out.
(B \ C) U (C \ B) = {0,2,4,6,8,10} U {1,3,5,7,9}
(B \ C) U (C \ B) = {0,2,4,6,8,10, 1,3,5,7,9}
(B \ C) U (C \ B) = {0,1,2,3,4,5,6,7,8,9,10}
Cardinality is 11
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d)
B = {0,2,4,6,8,10}
C = {1,3,5,7,9}
D = {0, 1, 10, 11}
B ∩ D = {0,10}
(B ∩ D) U C = {0,10} U {1,3,5,7,9}
(B ∩ D) U C = {0,10, 1,3,5,7,9}
(B ∩ D) U C = {0,1,3,5,7,9,10}
Cardinality is 7
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e)
Start with B = {0,2,4,6,8,10}
Erase elements found in set D. Those elements are 0 and 10
so we end up with B \ D = {2,4,6,8}
The cardinality of this new set is 4
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I'll let you handle the rest
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