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
Here are the solutions to the set theory problems: 1) Given the universal set U = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24\. a) Step 1: Identify square numbers less than 25. Square numbers are numbers obtained by squaring an integer. 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 (This is not less than 25) Step 2: List the elements of set A from the universal set U. The square numbers less than 25 that are in U are 1, 4, 9, 16. A = \1, 4, 9, 16\ b) Step 1: Identify odd numbers from the universal set U. Odd numbers are integers that are not divisible by 2. Step 2: List the elements of set O. The odd numbers in U are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23. O = \1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23\ c) Step 1: Identify composite numbers from the universal set U. A composite number is a positive integer that has at least one divisor other than 1 and itself. (Note: 1 is neither prime nor composite). Step 2: List the elements of set C. The composite numbers in U are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24. C = \4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24\ 2) Given the universal set U = \5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19\. a) Step 1: Identify even numbers from the universal set U. Even numbers are integers divisible by 2. Step 2: List the elements of set E. The even numbers in U are 6, 8, 10, 12, 14, 16, 18. E = \6, 8, 10, 12, 14, 16, 18\ b) Step 1: Identify multiples of 3 from the universal set U. Multiples of 3 are numbers that can be divided by 3 with no remainder. Step 2: List the elements of set M_3. The multiples of 3 in U are 6, 9, 12, 15, 18. M_3 = \6, 9, 12, 15, 18\ c) Step 1: Identify prime numbers from the universal set U. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Step 2: List the elements of set P. The prime numbers in U are 5, 7, 11, 13, 17, 19. P = \5, 7, 11, 13, 17, 19\ Last free one today — make it count tomorrow, or type /upgrade for unlimited.