If U={1,2,3,4,5,6,7,8}, A={2,4,6,8}, and B={1,2,3,4}, what is the value of (A∩B)'?
Answer and explanation
Correct answer: {1,3,5,6,7,8}
The common elements of A and B are 2 and 4, so A∩B={2,4}. The complement is taken relative to the stated universal set U. Therefore, remove 2 and 4 from U: (A∩B)'=U−{2,4}={1,3,5,6,7,8}. Hence option A is correct. Option B is the intersection itself, while options C and D omit or include elements incorrectly. This also agrees with De Morgan’s law: (A∩B)'=A'∪B'.
Frequently asked questions
What is the correct answer to this question?
{1,3,5,6,7,8}
Why is this the correct answer?
The common elements of A and B are 2 and 4, so A∩B={2,4}. The complement is taken relative to the stated universal set U. Therefore, remove 2 and 4 from U: (A∩B)'=U−{2,4}={1,3,5,6,7,8}. Hence option A is correct. Option B is the intersection itself, while options C and D omit or include elements incorrectly. This also agrees with De Morgan’s law: (A∩B)'=A'∪B'.
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.
