Let U = {x : x ∈ N, x ≤ 12} and A = {x ∈ U : x is a multiple of 3}. How many elements does A' have?
Answer and explanation
Correct answer: 8
Taking N as the positive natural numbers, U = {1, 2, ..., 12}, so |U| = 12. The multiples of 3 in U are A = {3, 6, 9, 12}, giving |A| = 4. The complement A' contains all members of U that are not multiples of 3. Therefore, |A'| = |U| − |A| = 12 − 4 = 8. Hence option C is correct. Listing the universal set first prevents confusion about which numbers are eligible for the complement.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Taking N as the positive natural numbers, U = {1, 2, ..., 12}, so |U| = 12. The multiples of 3 in U are A = {3, 6, 9, 12}, giving |A| = 4. The complement A' contains all members of U that are not multiples of 3. Therefore, |A'| = |U| − |A| = 12 − 4 = 8. Hence option C is correct. Listing the universal set first prevents confusion about which numbers are eligible for the complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
