If U = {1,2,3,4,5,6}, A = {1,2,3}, and B = {3,4,5}, what is Aᶜ ∪ Bᶜ?
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Answer and explanation
Correct answer: {1,2,4,5,6}
With respect to U, Aᶜ = {4,5,6} and Bᶜ = {1,2,6}. Taking their union gives every element appearing in either complement: {1,2,4,5,6}. This also follows from De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ, because A ∩ B = {3} and its complement in U is {1,2,4,5,6}. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1,2,4,5,6}
Why is this the correct answer?
With respect to U, Aᶜ = {4,5,6} and Bᶜ = {1,2,6}. Taking their union gives every element appearing in either complement: {1,2,4,5,6}. This also follows from De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ, because A ∩ B = {3} and its complement in U is {1,2,4,5,6}. Hence 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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