If the universal set is U = {1,2,3,4,5,6,7} and A = {1,4,7}, how many elements does Aᶜ ∪ A contain?
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Answer and explanation
Correct answer: 7
The complement Aᶜ contains all elements of U that are not in A, so Aᶜ = {2,3,5,6}. Taking the union with A gives {2,3,5,6} ∪ {1,4,7} = U. Thus Aᶜ ∪ A contains every element of the universal set, and its cardinality is |U| = 7. This is the standard identity A ∪ Aᶜ = U, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The complement Aᶜ contains all elements of U that are not in A, so Aᶜ = {2,3,5,6}. Taking the union with A gives {2,3,5,6} ∪ {1,4,7} = U. Thus Aᶜ ∪ A contains every element of the universal set, and its cardinality is |U| = 7. This is the standard identity A ∪ Aᶜ = U, so option C 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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