Question

Question 12 5 pts At the sci-fi club meeting of 34 people total, a show of hands revealed that 28 people are Star Wars fans, and 25 are Star Trek fans. There may be some people who are neither. What is the minimum number of people that must be both Star Trek and Star Wars fans? 5 pt Question 13 What is the step size of the recurrence relation an2 -3an + 5a-i ? 7 pt Question 14 Match the linear, constant-coefficient homogeneous recurrence relation, represented by its characteristic polynomial to the general solution of the recurrence. Two general solutions will remain unmatched

Answer 1

Given let u = Total number of people n(v) = 34 let A = star wars fans and B = star trek fans n(A) = 28, n(B) = 25 let N = neither a star war far nor a star trek fan let n(N) = p implies n[(A union B)'] = p we know that n(A union B)'] = 34 - p Also we know that n(A union B) = n(A) + n(B) - n(A intersection B) n(A intersection B) = n(A) + n(B) - n(A union B) \r\n n(A intersection B) = 28 + 25 - (34 - p) = 53 - 34 + p n(A intersection B) = 19 + p implies The minimum number of people that must be both star wars and star trek fans = minimum value of (19 + p) for p = 0 we get the minimum values therefore answer is 19