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Answer :
Final answer:
The union of the sets X = {4, 5, 7, 9} and Y = {} results in X cup Y = {4, 5, 7, 9}, because the empty set Y contributes no additional elements to the union.
Explanation:
In set theory, the union of two sets X and Y, denoted as X cup Y or X ∪ Y, includes all elements that are a part of set X, set Y, or both. Considering the provided sets where X = {4, 5, 7, 9} and Y = {}, the set Y is an empty set which means it contains no elements. Therefore, the union of set X and set Y is simply all the elements that are in set X since set Y does not contribute any elements. So X cup Y = {4, 5, 7, 9}, which corresponds to option A).
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