3.2.4. A function from S = {x, Y, z} to T = {1,2} can be written as a 2-by-3 array, such as (). (a) How many functions are there from S to T? Find all of them. (b) How many injections are there from S to T? Mark them in your answer to (a). (c) How many injections are there from T to S? Find all of them. (d) How many surjections are there from S to T? Mark them in your answer to (a). (e) How many surjections are there from T to S? Find all of them. (f) Guess the answers to (a) and (b) if S has m elements and T has n elements.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please answer a,b,c,d,e, and f for 3.2.4.

3.2.4. A function from S = {x, Y, z} to T = {1,2} can be written as a 2-by-3 array, such as ().
(a) How many functions are there from S to T? Find all of them.
(b) How many injections are there from S to T? Mark them in your answer to (a).
(c) How many injections are there from T to S? Find all of them.
(d) How many surjections are there from S to T? Mark them in your answer to (a).
(e) How many surjections are there from T to S? Find all of them.
(f) Guess the answers to (a) and (b) if S has m elements and T has n elements.
Transcribed Image Text:3.2.4. A function from S = {x, Y, z} to T = {1,2} can be written as a 2-by-3 array, such as (). (a) How many functions are there from S to T? Find all of them. (b) How many injections are there from S to T? Mark them in your answer to (a). (c) How many injections are there from T to S? Find all of them. (d) How many surjections are there from S to T? Mark them in your answer to (a). (e) How many surjections are there from T to S? Find all of them. (f) Guess the answers to (a) and (b) if S has m elements and T has n elements.
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