If U = {1, 2, ..., 18} and A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, what is (A')'?
Answer and explanation
Correct answer: A
The relevant governing concept is the double-complement law. For any subset A of a universal set U, A' contains exactly the elements of U outside A. Taking the complement again removes those outside elements and restores the original members of A, so (A')' = A. Although A is the set of even numbers from 2 through 18, the identity does not require listing them. Therefore option A is correct; A' is only the first complement, while U and ∅ are not generally the result.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
The relevant governing concept is the double-complement law. For any subset A of a universal set U, A' contains exactly the elements of U outside A. Taking the complement again removes those outside elements and restores the original members of A, so (A')' = A. Although A is the set of even numbers from 2 through 18, the identity does not require listing them. Therefore option A is correct; A' is only the first complement, while U and ∅ are not generally the result.
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.
