If A∩B=∅, n(A)=31, and n(B)=44, what is n(A∪B)?
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Answer and explanation
Correct answer: 75
A∩B=∅ means that A and B are disjoint, so they have no common elements. For any two sets, n(A∪B)=n(A)+n(B)−n(A∩B). Substituting the values gives 31+44−0=75. Since no element is counted in both sets, simple addition is valid. Therefore, option A is the correct union cardinality.
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
A∩B=∅ means that A and B are disjoint, so they have no common elements. For any two sets, n(A∪B)=n(A)+n(B)−n(A∩B). Substituting the values gives 31+44−0=75. Since no element is counted in both sets, simple addition is valid. Therefore, option A is the correct union cardinality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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