If U = {1,2,3,4,5,6,7,8,9,10} and A = {2,5,8}, how many elements are in Aᶜ ∪ {5}?
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Answer and explanation
Correct answer: 8
The complement Aᶜ contains all elements of U that are not in A. Therefore, Aᶜ = {1,3,4,6,7,9,10}, which has 7 elements. Since 5 is not in Aᶜ, taking the union with {5} adds one new element. Thus Aᶜ ∪ {5} has 7 + 1 = 8 elements, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The complement Aᶜ contains all elements of U that are not in A. Therefore, Aᶜ = {1,3,4,6,7,9,10}, which has 7 elements. Since 5 is not in Aᶜ, taking the union with {5} adds one new element. Thus Aᶜ ∪ {5} has 7 + 1 = 8 elements, so option A is correct.
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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