Q38 of 44 Page 1

If X and Y are two sets such that X has 8 elements, Y has 15 elements, and X∪Y has 18 elements, how many elements does X ∩ Y have?


We have n(X) = 8               n(Y) = 15 
       n(X ∪ Y) = 18
By using the formula,
     n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y)
We have 18 = 8 + 15 - n(X ∩ Y)
...  n(X ∩ Y) = 23 -18
...  n(X ∩ Y) = 5.

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