If A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}, and C = {6, 12, 18}, what is (A ∩ B) − C?
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Answer and explanation
Correct answer: ∅
First determine the intersection of A and B. The elements common to both sets are 6 and 12, so A ∩ B = {6, 12}. Now subtract C = {6, 12, 18}. Both elements of {6, 12} occur in C, so both are removed. No element remains, and therefore (A ∩ B) − C = ∅. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
First determine the intersection of A and B. The elements common to both sets are 6 and 12, so A ∩ B = {6, 12}. Now subtract C = {6, 12, 18}. Both elements of {6, 12} occur in C, so both are removed. No element remains, and therefore (A ∩ B) − C = ∅. Hence 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).
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