If \(A=\{1,2,3,4\}\) and \(B=\{4,5,6\}\), what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 6
The union of two sets contains every distinct element appearing in either set, but a common element is counted only once. Here, \(A\cup B=\{1,2,3,4,5,6\}\), so its cardinality is 6. Equivalently, \(n(A\cup B)=4+3-1=6\), because 4 belongs to both sets. Option B incorrectly counts 4 twice; options C and D do not represent the complete union.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The union of two sets contains every distinct element appearing in either set, but a common element is counted only once. Here, \(A\cup B=\{1,2,3,4,5,6\}\), so its cardinality is 6. Equivalently, \(n(A\cup B)=4+3-1=6\), because 4 belongs to both sets. Option B incorrectly counts 4 twice; options C and D do not represent the complete union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
