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Let U={0,1,2,3,4,5,6,7,8,9}, A={0,1,5,9}, B={0,1,2,3,4,5,6}, C={2,4,8}.
Find the set A∩(B∩C).

User Bergyman
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1 Answer

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Final answer:

The set A∩(B∩C) is asked, where U={0,1,2,3,4,5,6,7,8,9}. Find B∩C first which results in {2,4}; then find A∩{2,4}. Since A has no elements in common with {2,4}, A∩(B∩C) is an empty set, ∅.

Step-by-step explanation:

The student is asking to find the set A intersecting with the intersection of sets B and C (A∩(B∩C)), given the universal set U={0,1,2,3,4,5,6,7,8,9}.

Step 1: Identify the elements of each set. A={0,1,5,9}, B={0,1,2,3,4,5,6}, and C={2,4,8}.

Step 2: Find the intersection of sets B and C (B∩C). The elements common to both B and C are {2,4}.

Step 3: Now, find the intersection of set A with the intersection we found in Step 2, which is set {2,4} (A∩{2,4}). Since there are no elements common in A and {2,4}, the result is an empty set {} or ∅.

So, the set A∩(B∩C) is equal to ∅.

User Yeeling
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