If U = {1,2,3,4,5,6}, A = {1,2,3} and B = A', what is B'?
Answer and explanation
Correct answer: {1,2,3}
The complement B = A' is taken with respect to the universal set U. Since A = {1,2,3}, its complement is B = {4,5,6}. Taking the complement once more gives B' = (A')' = A, by the double-complement law. Therefore B' = {1,2,3}. Option B is B itself, not B', while option C is the universal set and option D is the empty set.
Frequently asked questions
What is the correct answer to this question?
{1,2,3}
Why is this the correct answer?
The complement B = A' is taken with respect to the universal set U. Since A = {1,2,3}, its complement is B = {4,5,6}. Taking the complement once more gives B' = (A')' = A, by the double-complement law. Therefore B' = {1,2,3}. Option B is B itself, not B', while option C is the universal set and option D is the empty set.
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.
