Let S be the set S = {a, b, c, d} and consider the function f : P(S) → Z given by f(X) = |X| Show that f is not one-to-one by writing down two distinct subsets X, Y ∈ P(S) that satisfy f(X) = f(Y). Write down a subset X that satisfies f(X) = 4 or explain why no such subset X exists. Write down a subset X that satisfies f(X) = 0 or explain why no such subset X exists.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Let S be the set S = {a, b, c, d} and consider the function f : P(S) → Z given by f(X) = |X|

Show that f is not one-to-one by writing down two distinct subsets X, Y ∈ P(S) that satisfy f(X) = f(Y).

Write down a subset X that satisfies f(X) = 4 or explain why no such subset X exists.

Write down a subset X that satisfies f(X) = 0 or explain why no such subset X exists.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,