13. Is the following proposition true or false? Justify your conclusion with a proof or a counterexample. If f:ST is a surjection and CCT, then f (f(C)) = C. 14 et f. S T Prove that CCA O B) = f(A O fB) for all subsets A and

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Just 13
12. Is the following proposition true or false? Justify your conclusion with a
proof or a counterexample.
If f:S T is an injection and ACS, then f S(A)) = A.
13. Is the following proposition true or false? Justify your conclusion with a
proof or a counterexample.
If f:S- T is a surjection and CCT, then f (f (C)) = C.
14. Let f: S T. Prove that f(AN B) = f(A) 0 f (B) for all subsets A and
B of S if and only if f is an injection.
I.
6.7 Chapter 6 Summary
Important Definitions
• Function, page 284
• Range of a function, page 287
• Domain of a function, page 285
• Image of a function, page 287
• Codomain of a function, page 285
• Equal functions, page 298
• Image of x under f. page 285
• Sequence, page 301
285
Iniection page 310
Transcribed Image Text:12. Is the following proposition true or false? Justify your conclusion with a proof or a counterexample. If f:S T is an injection and ACS, then f S(A)) = A. 13. Is the following proposition true or false? Justify your conclusion with a proof or a counterexample. If f:S- T is a surjection and CCT, then f (f (C)) = C. 14. Let f: S T. Prove that f(AN B) = f(A) 0 f (B) for all subsets A and B of S if and only if f is an injection. I. 6.7 Chapter 6 Summary Important Definitions • Function, page 284 • Range of a function, page 287 • Domain of a function, page 285 • Image of a function, page 287 • Codomain of a function, page 285 • Equal functions, page 298 • Image of x under f. page 285 • Sequence, page 301 285 Iniection page 310
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