If \(A\cap B=\varnothing\), \(n(A)=3\), and \(n(B)=5\), what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 8
For any two finite sets, \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Since \(A\cap B=\varnothing\), the sets are disjoint and their intersection has zero elements. Therefore, \(n(A\cup B)=3+5-0=8\). Option B counts only set B, option C counts only set A, and option D incorrectly multiplies the two cardinalities. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
For any two finite sets, \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Since \(A\cap B=\varnothing\), the sets are disjoint and their intersection has zero elements. Therefore, \(n(A\cup B)=3+5-0=8\). Option B counts only set B, option C counts only set A, and option D incorrectly multiplies the two cardinalities. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
