If X= {1,2,3,4} and Y = {3,5,6} , the elements of (XnY)UX are
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Correct Answer: Option 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\}.
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\}.