Functions and partial orders

Asked Oct 26 '16 at 20:35

Active Oct 26 '16 at 21:15

Viewed 22 times

I have the following statement to prove but not sure how to get started :

Let f: A → B and g: B → A be arbitrary functions. Show that there are subsets A₁, A₂ ⊆ A and B₁, B₂ ⊆ B such that : A₁ ∪ A₂ = A, A₁ ∩ A₂ = ∅ and B₁ ∪ B₂ = B, B₁ ∩ B₂ = ∅ and f(A₁) = B₁, g(B₂) = A₂.

I believe we need to use the notion of partial order here.

Thanks for your help.

edited Oct 26 '16 at 21:15

asked Oct 26 '16 at 20:35

TedMosby

1

Why did you say $g(A_2)$ when $g$ is not defined on $A$? – Stanley Oct 26 '16 at 21:09
My bad ! Let me edit this ! – TedMosby Oct 26 '16 at 21:15

Functions and partial orders

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