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If A(1)={2,3,4,5},A(2)={3,4,5,6},A(3)={4...

If `A_(1)={2,3,4,5},A_(2)={3,4,5,6},A_(3)={4,5,6,7}`, find `uuA_(i)andcapA_(i)`, where i={1,2,3}.

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To solve the problem, we need to find the union and intersection of the sets \( A_1, A_2, \) and \( A_3 \). Given: - \( A_1 = \{2, 3, 4, 5\} \) - \( A_2 = \{3, 4, 5, 6\} \) - \( A_3 = \{4, 5, 6, 7\} \) ### Step 1: Find the Union of the Sets The union of sets \( A_1, A_2, \) and \( A_3 \) is denoted as \( A_1 \cup A_2 \cup A_3 \). The union includes all distinct elements from all the sets. - Elements in \( A_1 \): \( 2, 3, 4, 5 \) - Elements in \( A_2 \): \( 3, 4, 5, 6 \) - Elements in \( A_3 \): \( 4, 5, 6, 7 \) Now, we combine all the elements and list them without repetition: \[ A_1 \cup A_2 \cup A_3 = \{2, 3, 4, 5, 6, 7\} \] ### Step 2: Find the Intersection of the Sets The intersection of sets \( A_1, A_2, \) and \( A_3 \) is denoted as \( A_1 \cap A_2 \cap A_3 \). The intersection includes only the elements that are present in all the sets. - Common elements in \( A_1 \), \( A_2 \), and \( A_3 \): - \( 4 \) is in \( A_1, A_2, \) and \( A_3 \) - \( 5 \) is in \( A_1, A_2, \) and \( A_3 \) Thus, the intersection is: \[ A_1 \cap A_2 \cap A_3 = \{4, 5\} \] ### Final Result - The union \( A_1 \cup A_2 \cup A_3 = \{2, 3, 4, 5, 6, 7\} \) - The intersection \( A_1 \cap A_2 \cap A_3 = \{4, 5\} \) ---
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