If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,8,9\}\), find \((A-B)\cup(A-C)\).
Answer and explanation
Correct answer: \(\{1,3,4,5,6\}\)
First calculate each difference separately. From \(A\), remove the elements also in \(B\): \(A-B=\{1,3,5\}\). From \(A\), remove the elements also in \(C\): \(A-C=\{3,4,5,6\}\). Their union contains every distinct element appearing in either result, namely \(\{1,3,4,5,6\}\). Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,4,5,6\}\)
Why is this the correct answer?
First calculate each difference separately. From \(A\), remove the elements also in \(B\): \(A-B=\{1,3,5\}\). From \(A\), remove the elements also in \(C\): \(A-C=\{3,4,5,6\}\). Their union contains every distinct element appearing in either result, namely \(\{1,3,4,5,6\}\). Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
