Ten kids line up for recess. The names of the kids are: {Abe, Ben, Cam Don, Eli,

Question

Ten kids line up for recess. The names of the kids are: {Abe, Ben, Cam Don, Eli, Fran, Gene Hal, Ike Jan}. Let S be the set of all possible ways to line up the kids. For example, one ordering might be: (Fran, Gene, Hal, Jan. Abe, Don, Cam Eli, Ike, Ben) The names are listed in order from left to right, so Fran is at the front of the line and Ben is at the end of the line. Let T be the set of all possible ways to line up the kids in which Gene is ahead of Don in the line. Note that Gene does not have to be immediately ahead of Don. For example, the ordering shown above is an element in T. Now define a function f whose domain is S and whose target is T. Let x be an element of S, so x is one possible way to order the kids. If Gene is ahead of Don the ordering x, then f(x) = x. If Don is ahead of Gene in x, then f (x) is the ordering that is the same as x, except that Don and Gene have swapped places. What is the output off on the following input? (Fran, Gene, Hal, Jan, Abe, Don, Cam Eli, Ike, Ben) What is the output of f on the following input? (Eli, Ike, Don, Hal, Jan, Abe Ben, Fran, Gene, Cam) Is the function f a bijection? Explain your answer. Is the function f a k-to-1 correspondence for some positive integer k? If so, for what value of k? Justify your answer.

Explanation / Answer

ans 6 : (Fran,Gene,Hal,Jan,Abe,Don,Cam,Eli,Ike,Ben)

ans 7 : (Eli,Ike,Gene,Hal,Jan,Abe,Ben,Fran,Don,Cam)

ans 8 : yes the function f a bijection because each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

ans 9 : yes the function f a k-to-1 correspondence for the positive integer 1.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.