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Examoogle • User • info@examoogle.com • EE-2024-8821
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If A = { 1, 2, 3, 4 }, B = { 3, 4, 5, 6 }, C = { 5, 6, 7, 8 }, find A ∩ (B ∪ C).
{3, 4}
{1, 2}
{5, 6}
{3, 4, 5, 6}
{3, 4}
Focus on the intersection A∩(B∪C) by first finding elements common to A in the union of B and C. Since A contains only {1, 2, 3, 4}, simply check which of these appear in either B or C.
Sets A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8}
A∩(B∪C)=(A∩B)∪(A∩C)
Focus on the intersection A∩(B∪C) by first finding elements common to A in the union of B and C. Since A contains only {1, 2, 3, 4}, simply check which of these appear in either B or C.
Students often perform the union B∪C first and then fail to filter the result by set A, or confuse intersection (common elements) with union (all elements combined).
Calculate Union of B and C
Perform the union operation B∪C, which collects all unique elements present in either B or C.
B∪C={3,4,5,6,7,8}
Calculate Intersection with A
Identify elements that are present in both A={1,2,3,4} and the result of the union {3,4,5,6,7,8}.
A∩{3,4,5,6,7,8}={3,4}
A is correct because the elements 3 and 4 are the only members of set A that are also present in the union of sets B and C.
This concept of set operations is foundational for Probability theory (Venn diagrams) and Boolean algebra in Digital Electronics.