Discussion
If X = { 2, 3, 4, 5 } and Y = {3, 4, 5, 6} be two sets then X ∪ Y contains the number of elements
Answer: C
X ∪ Y contains 5 elements.
The union contains every element that is in X or Y or both, each counted once:
\[ X \cup Y = \{2, 3, 4, 5, 6\} \]
That is 5 elements. 4 is the size of either set on its own, 7 counts some shared elements twice, and 3 is the size of the intersection, {3, 4, 5}, not the union.
The formula gives the same result: \(n(X \cup Y) = n(X) + n(Y) - n(X \cap Y) = 4 + 4 - 3 = 5\).
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