Question 184847
# 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}