Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let X and Y be sets. Let us say that a subset S of the cartesian product X x Y is a rectangle if S = A × B for some A C X and BCY. 10. (a) Prove that every one-element subset of X x Y is a rectangle. (b) Prove that whenever X is a set with more than one element, the subset {(x, æ) : ¤ € X} S = of X x X is not a rectangle. (Here Y = X.) (c) Is the union of two rectangles in X x Y always a rectangle? Give either a proof that this is true or an example to show that it is false.

Let X and Y be sets. Let us say that a subset S of the cartesian product X x Y is a rectangle if S = A × B for some A C X and BCY. 10. (a) Prove that every one-element subset of X x Y is a rectangle. (b) Prove that whenever X is a set with more than one element, the subset {(x, æ) : ¤ € X} S = of X x X is not a rectangle. (Here Y = X.) (c) Is the union of two rectangles in X x Y always a rectangle? Give either a proof that this is true or an example to show that it is false.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Let X and Y be sets. Let us say that a subset S of the cartesian product X x Y is a rectangle if S = A × B for some A C X and BCY. 10. (a) Prove that every one-element subset of X x Y is a rectangle. (b) Prove that whenever X is a set with more than one element, the subset {(x, æ) : ¤ € X} S = of X x X is not a rectangle. (Here Y = X.) (c) Is the union of two rectangles in X x Y always a rectangle? Give either a proof that this is true or an example to show that it is false.
Transcribed Image Text:Let X and Y be sets. Let us say that a subset S of the cartesian product X x Y is a rectangle if S = A × B for some A C X and BCY. 10. (a) Prove that every one-element subset of X x Y is a rectangle. (b) Prove that whenever X is a set with more than one element, the subset {(x, æ) : ¤ € X} S = of X x X is not a rectangle. (Here Y = X.) (c) Is the union of two rectangles in X x Y always a rectangle? Give either a proof that this is true or an example to show that it is false.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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,
SEE MORE TEXTBOOKS