I'd really like some help in answering the next question...anything that might help will save my life:
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F is defined this way: F:A→B where [FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Main]⊂[/FONT][FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]N[/FONT][FONT=MathJax_Main])[/FONT] where P(N) is the power set of the naturals.[/FONT]
Let [FONT=MathJax_Math-italic]S[FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]R[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Math-italic]A[/FONT] such that [FONT=MathJax_Math-italic]S[/FONT] is a proper subset of [FONT=MathJax_Math-italic]R[/FONT] if and only if [FONT=MathJax_Math-italic]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]S[/FONT][FONT=MathJax_Main])[/FONT] is a proper subset of [FONT=MathJax_Math-italic]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]R[/FONT][FONT=MathJax_Main])[/FONT]
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Questions:
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F is defined this way: F:A→B where [FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Main]⊂[/FONT][FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]N[/FONT][FONT=MathJax_Main])[/FONT] where P(N) is the power set of the naturals.[/FONT]
Let [FONT=MathJax_Math-italic]S[FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]R[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_Math-italic]A[/FONT] such that [FONT=MathJax_Math-italic]S[/FONT] is a proper subset of [FONT=MathJax_Math-italic]R[/FONT] if and only if [FONT=MathJax_Math-italic]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]S[/FONT][FONT=MathJax_Main])[/FONT] is a proper subset of [FONT=MathJax_Math-italic]F[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]R[/FONT][FONT=MathJax_Main])[/FONT]
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Questions:
- Is there an [FONT=MathJax_Math-italic]F[/FONT] from [FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_AMS]N[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_AMS]∖[/FONT][FONT=MathJax_AMS]N[/FONT]to [FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_AMS]N[/FONT][FONT=MathJax_Main])[/FONT]which is also a surjective function?
- Is there an [FONT=MathJax_Math-italic]F[/FONT] from [FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_AMS]N[/FONT][FONT=MathJax_Main])[/FONT] to [FONT=MathJax_Math-italic]P[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_AMS]N[/FONT][FONT=MathJax_Main])[/FONT] where [FONT=MathJax_Math-italic]F[/FONT] is a surjective function yet not the identity function?