Which functions are missing from {1,2,3} to {a,b} and why?

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In summary, the conversation discusses the number of functions from a set of three elements to a set of two elements, and the concepts of injective and surjective functions. The formula n^m is used to determine the number of functions, with n being the number of elements in the second set and m being the number of elements in the first set. The conversation also acknowledges that the formula may yield a different number of functions than expected due to confusion about which functions are included. It is concluded that there are eight functions in total, with two being injective and none being surjective.
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Kingyou123
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Homework Statement


How many functions are there from {1,2,3} to {a,b}? Which are injective? Which are surjective?

Homework Equations


n^m. gives the number of functions

The Attempt at a Solution


To me the number of functions that can be made are 6 because 3x2=6 but I have read online that n^m, n being the elements in the second set and m being the number of elements in the first set, gives you the number of functions. That equation gives me 8 functions but for the life of me I can't figure which functions I'm leaving out.
20160221_200842.jpg

Also there can't be any injective functions because f(1) can take 2 values and f(2) can take one value. Leaving f(3) with none so therefore It can't be injective,correct?
 
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  • #2
Kingyou123 said:

Homework Statement


How many functions are there from {1,2,3} to {a,b}? Which are injective? Which are surjective?

Homework Equations


n^m. gives the number of functions

The Attempt at a Solution


To me the number of functions that can be made are 6 because 3x2=6 but I have read online that n^m, n being the elements in the second set and m being the number of elements in the first set, gives you the number of functions. That equation gives me 8 functions but for the life of me I can't figure which functions I'm leaving out.
You are missing two functions for which 1 → b .
View attachment 96266
Also there can't be any injective functions because f(1) can take 2 values and f(2) can take one value. Leaving f(3) with none so therefore It can't be injective,correct?
 
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  • #3
SammyS said:
You are missing two functions for which 1 → b .
Thank you, was my explanation for injective correct?
 
  • #4
Kingyou123 said:
Thank you, was my explanation for injective correct?
Yes
 
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  • #5
SammyS said:
Yes
Awesome thank you :)
 

FAQ: Which functions are missing from {1,2,3} to {a,b} and why?

What is the purpose of asking "Which functions am I missing?"

The purpose of asking this question is to identify any gaps in the functions available for a specific task or project. By knowing which functions are missing, a scientist can determine if there are any limitations or areas that need improvement in their research or experiment.

How can I determine which functions I am currently missing?

To determine which functions are missing, it is important to first have a clear understanding of what functions are needed for the task or project. Then, one can review the available functions and compare them to the needed functions, identifying any gaps or missing functions.

Are there any resources or tools available to help identify missing functions?

Yes, there are resources and tools available to help identify missing functions. These can include reference materials, online databases, and software programs that provide a comprehensive list of functions and their descriptions.

What should I do if I discover that I am missing important functions?

If you discover that you are missing important functions, you should first try to find alternative functions that can serve a similar purpose. If that is not possible, you may need to develop or create new functions to fill the gap. You can also seek advice from other scientists or experts in the field for suggestions.

Is it possible that I am missing functions that I am not aware of?

Yes, it is possible that you may be missing functions that you are not aware of. This is why it is important to continually review and update your knowledge on available functions and their applications. It is also helpful to collaborate and share ideas with other scientists to learn about new functions and techniques.

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