This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back alishabayambumagar — missed you this week. Here are the sets formed from whole numbers up to 20 (i.e., \0, 1, 2, , 20\) in both listing and set-builder forms: a) (i) Set of composite numbers Step 1: Identify composite numbers up to 20. Composite numbers are natural numbers greater than 1 that are not prime. Listing form: \4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20\ Set-builder form: \x x is a composite number and 0 x 20\ (ii) Set of prime numbers Step 1: Identify prime numbers up to 20. Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Listing form: \2, 3, 5, 7, 11, 13, 17, 19\ Set-builder form: \x x is a prime number and 0 x 20\ (iii) Set of even numbers Step 1: Identify even numbers up to 20. Even numbers are integers divisible by 2. Listing form: \0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20\ Set-builder form: \x x is an even number and 0 x 20\ (iv) Set of odd numbers Step 1: Identify odd numbers up to 20. Odd numbers are integers not divisible by 2. Listing form: \1, 3, 5, 7, 9, 11, 13, 15, 17, 19\ Set-builder form: \x x is an odd number and 0 x 20\ (v) Set of square numbers Step 1: Identify square numbers up to 20. These are numbers that are the square of an integer. Listing form: \0, 1, 4, 9, 16\ Set-builder form: \x x = n^2, n W, 0 n^2 20\ (vi) Set of cube numbers Step 1: Identify cube numbers up to 20. These are numbers that are the cube of an integer. Listing form: \0, 1, 8\ Set-builder form: \x x = n^3, n W, 0 n^3 20\ (vii) Set of multiples of 5 Step 1: Identify multiples of 5 up to 20. These are numbers that can be divided by 5 without a remainder. Listing form: \0, 5, 10, 15, 20\ Set-builder form: \x x is a multiple of 5 and 0 x 20\ (viii) Set of factors of 20 Step 1: Identify factors of 20. These are positive integers that divide 20 evenly. Listing form: \1, 2, 4, 5, 10, 20\ Set-builder form: \x x is a factor of 20\ Drop the next question! 📸