Question 1008189
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