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
2B, Question 1: The universal set is the set of integers from 1 to 20 inclusive. So, = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\. i. A = all even numbers Step 1: Identify all even numbers within the universal set . Even numbers are integers divisible by 2. A = \2, 4, 6, 8, 10, 12, 14, 16, 18, 20\ The elements of set A are \2, 4, 6, 8, 10, 12, 14, 16, 18, 20\. ii. B = all prime numbers Step 2: Identify all prime numbers within the universal set . Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. B = \2, 3, 5, 7, 11, 13, 17, 19\ The elements of set B are \2, 3, 5, 7, 11, 13, 17, 19\. iii. C = all perfect squares Step 3: Identify all perfect squares within the universal set . Perfect squares are numbers that can be expressed as the square of an integer. 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 (This is greater than 20, so it is not in ) C = \1, 4, 9, 16\ The elements of set C are \1, 4, 9, 16\. iv. D = all perfect cubes Step 4: Identify all perfect cubes within the universal set . Perfect cubes are numbers that can be expressed as the cube of an integer. 1^3 = 1 2^3 = 8 3^3 = 27 (This is greater than 20, so it is not in ) D = \1, 8\ The elements of set D are \1, 8\. v. E = all odd numbers Step 5: Identify all odd numbers within the universal set . Odd numbers are integers not divisible by 2. E = \1, 3, 5, 7, 9, 11, 13, 15, 17, 19\ The elements of set E are \1, 3, 5, 7, 9, 11, 13, 15, 17, 19\. That's 2 down. 3 left today — send the next one.