If U = {1,2,3,4,5,6,7,8,9,10} and A = {2,3,5,7}, what type of set is A′?
Answer and explanation
Correct answer: Composite numbers and 1
The set A contains all prime numbers from 1 to 10: 2, 3, 5, and 7. The complement A′ is taken relative to the universal set U, so it contains the elements of U that are not in A. Removing those four primes leaves {1,4,6,8,9,10}. These are the composite numbers 4, 6, 8, 9, and 10 together with 1. Since 1 is neither prime nor composite, the correct description is composite numbers and 1.
Frequently asked questions
What is the correct answer to this question?
Composite numbers and 1
Why is this the correct answer?
The set A contains all prime numbers from 1 to 10: 2, 3, 5, and 7. The complement A′ is taken relative to the universal set U, so it contains the elements of U that are not in A. Removing those four primes leaves {1,4,6,8,9,10}. These are the composite numbers 4, 6, 8, 9, and 10 together with 1. Since 1 is neither prime nor composite, the correct description is composite numbers and 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
