If n(U)=210, n(A∩B)=52, and n(Aᶜ∪Bᶜ)=170, what can be said about the given data?
Answer and explanation
Correct answer: The data are inconsistent
By De Morgan’s law, Aᶜ∪Bᶜ=(A∩B)ᶜ. The complement of A∩B in the universal set must therefore contain 210−52=158 elements. However, the question states that n(Aᶜ∪Bᶜ)=170. Because 158 and 170 are different, the two supplied values cannot describe the same sets; hence the data are inconsistent.
Frequently asked questions
What is the correct answer to this question?
The data are inconsistent
Why is this the correct answer?
By De Morgan’s law, Aᶜ∪Bᶜ=(A∩B)ᶜ. The complement of A∩B in the universal set must therefore contain 210−52=158 elements. However, the question states that n(Aᶜ∪Bᶜ)=170. Because 158 and 170 are different, the two supplied values cannot describe the same sets; hence the data are inconsistent.
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.
