If \(A=B\), then in a Venn diagram, \(A-B\) will be equal to which of the following?
Answer and explanation
Correct answer: \(\varnothing\)
The difference \(A-B\) consists of elements that belong to A but do not belong to B. Since \(A=B\), every element of A is also in B, so there can be no element left in A after removing B. Symbolically, \(A-B=A\cap B^c=A\cap A^c=\varnothing\). Therefore, the correct answer is the empty set, option C. It is not A or B because the two sets are identical, and it is not the universal set U because no element outside the sets is included in the difference.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The difference \(A-B\) consists of elements that belong to A but do not belong to B. Since \(A=B\), every element of A is also in B, so there can be no element left in A after removing B. Symbolically, \(A-B=A\cap B^c=A\cap A^c=\varnothing\). Therefore, the correct answer is the empty set, option C. It is not A or B because the two sets are identical, and it is not the universal set U because no element outside the sets is included in the difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
