Question

9. Prove that if A and B are finite sets with |A| = |B|, then any injection f : A → B is also a surjection. Show this is not necessarily true if A and B are not finite. 10. Prove that if A and B are finite sets with |A| = |B|, then any surjection f : A → B is also an injection. Show this is not necessarily true if A and B are not finite

Name: 9 prove that if a and b are finite sets with a b then any injection f a b is also a surjection show this is not necessarily true if a and b are not finite 10 prove that if a and b are finite 44988
Uploaded: 2022-12-10T02:12:31-08:00
Duration: 4 min 42 s
Channel: Vincenzo Zaccaro
Description: 9 prove that if a and b are finite sets with a b then any injection f a b is also a surjection show this is not necessarily true if a and b are not finite 10 prove that if a and b are finite 44988

          9. Prove that if A and B are
finite sets with |A| =
|B|, then any injection f :
A → B is
also a surjection. Show this is not necessarily true if
A and B are not finite.
10. Prove that if A and B are
finite sets with |A| =
|B|, then any surjection f :
A → B
is also an injection. Show this is not necessarily true if
A and B are not finite

Added by Patrick S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

12/10/2022

Step 1

Step 1: Given that A and B are finite sets with |A| = |B|, and f : A → B is an injection, we want to prove that f is also a surjection. Show more…

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9. Prove that if A and B are finite sets with |A| = |B|, then any injection f : A → B is also a surjection. Show this is not necessarily true if A and B are not finite. 10. Prove that if A and B are finite sets with |A| = |B|, then any surjection f : A → B is also an injection. Show this is not necessarily true if A and B are not finite