If U={1,2,3,4,5,6,7,8,9,10} and Aᶜ={1,4,9}, how many elements does A contain?
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Answer and explanation
Correct answer: 7
For a finite universal set, A and Aᶜ are disjoint and together contain every element of U. Therefore, n(A)+n(Aᶜ)=n(U). Here n(U)=10 and Aᶜ={1,4,9}, so n(Aᶜ)=3. Thus n(A)=10−3=7. In fact, A is {2,3,5,6,7,8,10}, which visibly contains seven elements. Option B counts the complement rather than A.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For a finite universal set, A and Aᶜ are disjoint and together contain every element of U. Therefore, n(A)+n(Aᶜ)=n(U). Here n(U)=10 and Aᶜ={1,4,9}, so n(Aᶜ)=3. Thus n(A)=10−3=7. In fact, A is {2,3,5,6,7,8,10}, which visibly contains seven elements. Option B counts the complement rather than A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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