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If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}, find A ∩ (B ∪ C).
{7, 9, 11}
{3, 5, 7, 9, 11}
{5, 7, 9, 11}
{3, 7, 9, 11}
{7, 9, 11}
Identify elements common to A and (B or C). Focus only on elements present in A, then check if they exist in either B or C.
Sets are A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, and C = {11, 13, 15}.
A∩(B∪C)=(A∩B)∪(A∩C)
Identify elements common to A and (B or C). Focus only on elements present in A, then check if they exist in either B or C.
Confusing union (∪) with intersection (∩) or mistakenly performing the operations in the wrong order of precedence.
Calculate Union of B and C
First, find the union of sets B and C, which includes all unique elements present in either set.
B∪C={7,9,11,13,15}
Calculate Intersection with A
Find the intersection of set A with the result of (B ∪ C). This involves selecting only those elements that appear in both sets.
A∩{7,9,11,13,15}={7,9,11}
A is correct because the elements 7, 9, and 11 are the only numbers present in set A that are also contained in the union of sets B and C.
Understanding Venn diagrams makes solving set operations faster and helps in visualizing complex overlapping regions in probability questions.