If X= {1,2,3,4} and Y = {3,5,6} , the elements of (XnY)UX are
A. {1,2,3,4} B. {3,5,6} C. {3} D. {1,2,4}
Correct Answer: A
Explanation
Let's evaluate the expression \((X \cap Y) \cup X\) where \( X = \{1, 2, 3, 4\} \) and \( Y = \{3, 5, 6\} \).
1. Find \( X \cap Y \) (the intersection of X and Y): - The intersection includes elements common to both sets. - \( X \cap Y = \{3\} \)
2. Find \((X \cap Y) \cup X\) (the union of \( X \cap Y \) and X): - The union includes all elements from both sets, with duplicates removed. - \( (X \cap Y) \cup X = \{3\} \cup \{1, 2, 3, 4\} \) - Combining these, we get \( \{1, 2, 3, 4\} \)
Thus, the elements of \((X \cap Y) \cup X\) are A. \{1, 2, 3, 4\}.