Please give detailed explanations to the solutions for the following three probl
ID: 3862971 • Letter: P
Question
Please give detailed explanations to the solutions for the following three problems. Thanks in advance.
1. Let f (x) = ax+b and g(x) = cx+d where a, b. c, and d are constants. Determine for which constants a, b, c, and d it is true that f.g = g.f.
A. (a-1)d = (c-1)b
B. (a+d) = (c-1)b
C. ad + b = cb - d
D. ad + b = cb + d
2. Could the following table represent relations in a relational database?
Cast list
Character Actor Understudy
Hamlet Helmut Weiner John Garner, Sam Ranier
Claudius Richard Gunther Bob Searle
Ophelia Suzanne Bonner Sally Richards
Gertrude Virginia Smith No understudy
A. True
B. False
3. Form the projection (Teaching assignments) [course, instructor]
Teaching Assignments
Course Section Semester Instructor
MAT 241 1 Fall Gossett
MAT 241 2 Fall Gossett
MAT 222 1 Winter Kinney
MAT124M 1 Fall Conrath
MAT124M 2 Fall Kinney
A. course: MAT 241, MAT 241, MAT 222, MAT124M, MAT124M; instructor: Gossett, Gossett, Kinnery, Conrath, Kinney
B. course: MAT 241, MAT 222, MAT124M; instructor: Gossett, Kinnery, Conrath
C. course: MAT 241, MAT 222, MAT124M, MAT124M; instructor: Gossett, Kinnery, Conrath, Kinney
Explanation / Answer
1. All of the above
f.g = acx^2 + (ad + bc)x + bd
g.f = acx^2 + (bc + ad)x + bd
so, for any value of a,b,c and d, f.g = g.f
2 A. true. The table represents the relation character -> Actor and character -> Understudy
3 C. course: MAT 241, MAT 222, MAT124M, MAT124M; instructor: Gossett, Kinnery, Conrath, Kinney
duplicates are not projected.