Question 143198This question is from textbook Survey of Math w/ Apllications
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7. (3 pts) 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 Survey of Math w/ Apllications
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! If K has 30 elements and 11 of them are in common with J, then K has 30 - 11 = 19 elements that are NOT in common with J. Likewise, J has 35 elements that are NOT in common with K.
The union of K and J consists of the elements of K not in common with J plus the elements of J not in common with K plus the elements that are common to both, so n = 19 + 35 + 11 = 65.
Another way to look at it is to say K has 30 elements and J has 46 elements and the sum is 76, but since they have 11 elements in common, adding the number of elements in the 2 sets means that you have counted 11 elements twice, so the number of elements in the union is 76 minus 11 = 65. This method works fine for two sets, but gets horribly complicated when you try to figure the union of 3 or more sets, therefore the first method is a better general solution to this type of problem.
Super Double Plus Extra Credit: Find m(K∩J)
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