3. Let A be a set and P(A) the power set of A. Complete the following proof that there is no onto function from A to P(A). Proof: Suppose (for contradiction) that f: A P(A) is an onto function. Consider the set B = {x € A| r 4 f(x)}. If f is onto, then for all CE P(A), there must be an element r E A so that f(x) = C. BCA so BE P(A), so there is an element r E A so that f(x) = B. %3D Question: is x E B or r 4 B? 4. Prove that for all n E N, 7" +2 is divisible by 3.
3. Let A be a set and P(A) the power set of A. Complete the following proof that there is no onto function from A to P(A). Proof: Suppose (for contradiction) that f: A P(A) is an onto function. Consider the set B = {x € A| r 4 f(x)}. If f is onto, then for all CE P(A), there must be an element r E A so that f(x) = C. BCA so BE P(A), so there is an element r E A so that f(x) = B. %3D Question: is x E B or r 4 B? 4. Prove that for all n E N, 7" +2 is divisible by 3.
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
complete handwritten solution for Q 3
Transcribed Image Text:3.
Let A be a set and P(A) the power set of A.
Complete the following proof that there is no onto function from A to P(A).
Proof: Suppose (for contradiction) that f : A→ P(A) is an onto function.
Consider the set B =
{x € A|x¢ f()}.
If f is onto, then for all C E P(A),
there must be an element r E A so that f(x) = C.
BCA so BE P(A), so there is an element x E A so that f(x) = B.
%3D
Question: is x E B or r 4 B?
1
4.
Prove that for all n E N, 7" +2 is divisible by 3.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
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,
