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
You're on a roll — here's the solution for the next part of your question. Part 1: Sets A and B Given sets: A = \2, 3, 4, 5, 6, 7, 8, 9\ B = \2, 3, 5, 7\ Step 1: Find the common elements (intersection) of A and B. The elements that are present in both set A and set B are 2, 3, 5, and 7. A B = \2, 3, 5, 7\ Step 2: Draw a Venn diagram for sets A and B. Since all elements of B are also in A, set B is a subset of set A. This means the circle representing B should be drawn entirely inside the circle representing A. Place the elements common to both A and B (which are all elements of B) inside the inner circle (B): \2, 3, 5, 7\. Place the elements that are in A but not in B in the region of circle A outside circle B: \4, 6, 8, 9\. Here is the Venn diagram: (0,0) circle (2cm) node[above right] A; (0,0) circle (1cm) node[above right] B; at (0, 0.5) 2; at (-0.5, 0) 3; at (0.5, 0) 5; at (0, -0.5) 7; at (1.5, 1.5) 4; at (-1.5, 1.5) 6; at (1.5, -1.5) 8; at (-1.5, -1.5) 9; Part 2: Sets P and Q Given sets: P = \x : x is a prime number less than 10\ Q = \y : y is an even number less than ...\ (The definition for Q is cut off, assuming "less than 10") Step 1: List the elements of set P. Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers less than 10 are 2, 3, 5, and 7. P = \2, 3, 5, 7\ Step 2: List the elements of set Q (assuming "less than 10"). Even numbers are integers divisible by 2. The even numbers less than 10 are 0, 2, 4, 6, and 8. Q = \0, 2, 4, 6, 8\ What's next? Send 'em!