Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Editing Proof Let A, B be finite sets, and letf:A B be a function. Then: ii) If fis surjective, then 4| B| Proof: Let B-{b,, b2, b3, . . ., bm}, so B = m. Assume that f:A→B is onto and that B|> |4|. Since fis onto, for each i = 1, 2, ..., m we can find an %3D %3D element in A such that f(a) = b, Since B > LA|, there must exist some i + k, so that a, = a; = x, and so we would have f (x) = b, and also f(x) = b;. This is a contradiction, because it would mean that fis not really a function. Thus, we must have B < L4|

Editing Proof Let A, B be finite sets, and letf:A B be a function. Then: ii) If fis surjective, then 4| B| Proof: Let B-{b,, b2, b3, . . ., bm}, so B = m. Assume that f:A→B is onto and that B|> |4|. Since fis onto, for each i = 1, 2, ..., m we can find an %3D %3D element in A such that f(a) = b, Since B > LA|, there must exist some i + k, so that a, = a; = x, and so we would have f (x) = b, and also f(x) = b;. This is a contradiction, because it would mean that fis not really a function. Thus, we must have B < L4|

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section1.8: The Coordinate Plane
Problem 13E
See similar textbooks
icon
Related questions
Question
Chapter 7- Func Vwng Mark Bentemas scre Options A Beintema, Mark Settings : Exit Fu Transitions Animations Slide Show Review View Help A Share P Com 2 Shape Fill- PFind Replace - A A A 三 。 中。 2 Shape Outline US b AV- Aa- 2-A- Shapes Arrange Quick Dictate Design Ideas Styles - O Shape Effects - A Select - Font Paragraph Drawing Editing Voice Designer Proof Let A, B be finite sets, and let f:A B be a function. Then: ii) If fis surjective, then 4| B| I Mark Beintema Proof: Let B={b,, b2, b3, . . ., bm, so B m. Assume that f: A→B is onto and that B > \A|]. Since fis onto, for each i = 1, 2, ..., m we can find an element a, in A such that f(a) = b, Since B > A, there must exist some i± k, so that a, = a; = x, and so we would have f (x) = b, and also f(x) = b;- This is a contradiction, because it would mean that fis not really a function. Thus, we must have B <L4 Leave Participants Chat Share & 2$4 8 6 !!! lili 口
Transcribed Image Text:Chapter 7- Func Vwng Mark Bentemas scre Options A Beintema, Mark Settings : Exit Fu Transitions Animations Slide Show Review View Help A Share P Com 2 Shape Fill- PFind Replace - A A A 三 。 中。 2 Shape Outline US b AV- Aa- 2-A- Shapes Arrange Quick Dictate Design Ideas Styles - O Shape Effects - A Select - Font Paragraph Drawing Editing Voice Designer Proof Let A, B be finite sets, and let f:A B be a function. Then: ii) If fis surjective, then 4| B| I Mark Beintema Proof: Let B={b,, b2, b3, . . ., bm, so B m. Assume that f: A→B is onto and that B > \A|]. Since fis onto, for each i = 1, 2, ..., m we can find an element a, in A such that f(a) = b, Since B > A, there must exist some i± k, so that a, = a; = x, and so we would have f (x) = b, and also f(x) = b;- This is a contradiction, because it would mean that fis not really a function. Thus, we must have B <L4 Leave Participants Chat Share & 2$4 8 6 !!! lili 口
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Limits and Continuity
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
SEE MORE TEXTBOOKS