Solve the simultaneous equations and set theory problems: 1) x + 2y = 7 and 2x - 2y = 2. 2) P = primes < 15, Q = even numbers < 15. Find P U Q and if P, Q are disjoint.

Here's the solution to question 3: 3a. To solve the simultaneous equations: 1) x + 2y = 7 2) 2x - 2y = 2 Step 1: Add equation (1) and equation (2) to eliminate y. (x + 2y) + (2x - 2y) = 7 + 2 3x = 9 Step 2: Solve for x. x = (9)/(3) x = 3 Step 3: Substitute the value of x=3 into equation (1). 3 + 2y = 7 Step 4: Solve for y. 2y = 7 - 3 2y = 4 y = (4)/(2) y = 2 The solution is x=3, y=2. 3b. Consider the sets: P = \x : x is a prime number less than 15\ Q = \x : x is an even number less than 15\ i) List all the elements of sets P and Q: Prime numbers less than 15 are numbers greater than 1 that are only divisible by 1 and themselves. P = \2, 3, 5, 7, 11, 13\ Even numbers less than 15 are integers divisible by 2. Q = \2, 4, 6, 8, 10, 12, 14\ ii) Find P U Q: The union of P and Q includes all elements present in either set, without repetition. P Q = \2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14\ iii) State whether P and Q are disjoint sets: Disjoint sets have no common elements (their intersection is an empty set). The intersection of P and Q is P Q = \2\, since 2 is in both sets. Since P Q ≠ , the sets P and Q are not disjoint.