SOLUTION: Set K contains 30 elements, set J contains 46 elements, and 11 elements are common to both sets. Find n ( K U J).

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Question 184510This question is from textbook A Survey of Mathematics with Application
: Set K contains 30 elements, set J contains 46 elements, and 11 elements are common to both sets. Find n ( K U J). This question is from textbook A Survey of Mathematics with Application

Answer by jim_thompson5910(21685) About Me  (Show Source):
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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