Ten kids line up for recess. The names of the kids are: {Alex, Bobby, Cathy, Dave, Emy, Frank, George, Homa, Ian, Jim}. Let S be the set of all possible ways to line up the kids. For example, one order might be: (Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby) The names are listed in order from left to right, so Frank is at the front of the line and Bobby is at the end of the line. Let T be the set of all possible ways to line up the kids in which George is ahead of Dave in the line. Note that George does not have to be immediately ahead of Dave. For example, the ordering shown above is an element in T. Now define a funetion f whose domain is S and whose target is T. Let æ be an element of S, so x is one possible way to order the kids. If George is ahead of Dave in the ordering æ, then f(x) = x. If Dave is ahead of George in r, then f(x) is the ordering that is the same as r, except that Dave and George have swapped places. (a) What is the output of f on the following input? (Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby) (b) What is the output of f on the following input? (Emy, Ian, Dave, Homa, Jim, Alex, Bobby, Frank, George, Cathy) (c) Is the function f a k-to-1 correspondence for some positive integer k? If so, for what value of k? Justify your answer.
Ten kids line up for recess. The names of the kids are: {Alex, Bobby, Cathy, Dave, Emy, Frank, George, Homa, Ian, Jim}. Let S be the set of all possible ways to line up the kids. For example, one order might be: (Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby) The names are listed in order from left to right, so Frank is at the front of the line and Bobby is at the end of the line. Let T be the set of all possible ways to line up the kids in which George is ahead of Dave in the line. Note that George does not have to be immediately ahead of Dave. For example, the ordering shown above is an element in T. Now define a funetion f whose domain is S and whose target is T. Let æ be an element of S, so x is one possible way to order the kids. If George is ahead of Dave in the ordering æ, then f(x) = x. If Dave is ahead of George in r, then f(x) is the ordering that is the same as r, except that Dave and George have swapped places. (a) What is the output of f on the following input? (Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby) (b) What is the output of f on the following input? (Emy, Ian, Dave, Homa, Jim, Alex, Bobby, Frank, George, Cathy) (c) Is the function f a k-to-1 correspondence for some positive integer k? If so, for what value of k? Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:PROBLEM 2
Ten kids line up for recess. The names of the kids are:
{Alex, Bobby, Cathy, Dave, Emy, Frank, George, Homa, Ian, Jim}.
Let S be the set of all possible ways to line up the kids. For example, one order
might be:
(Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby)
The names are listed in order from left to right, so Frank is at the front of the
line and Bobby is at the end of the line.
Let T be the set of all possible ways to line up the kids in which George is ahead
of Dave in the line. Note that George does not have to be immediately ahead of
Dave. 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 George is ahead of Dave
in the ordering x, then f(x) = x. If Dave is ahead of George in x, then f(x) is the
ordering that is the same as r, except that Dave and George have swapped places.
(a) What is the output of f on the following input?
(Frank, George, Homa, Jim, Alex, Dave, Cathy, Emy, Ian, Bobby)
(b) What is the output of f on the following input?
(Emy, Ian, Dave, Homa, Jim, Alex, Bobby, Frank, George, Cathy)
(c) Is the function f a k-to-l correspondence for some positive integer k? If
so, for what value of k? Justify your answer.
(d) There are 3628800 ways to line up the 10 kids with no restrictions on who
comes before whom. That is, |S| = 3628800. Use this fact and the answer
to the previous question to determine |T|.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
