Soit-f-E-F-une-application-P-E-est-l-ensemble-des-parties-de-E-Montrer-que-f-est-injective-A-P-E-A-f-1-f-A-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 161204 by mathocean1 last updated on 14/Dec/21

Soit f: E→F , une application. P(E) est l′ensemble des parties de E. Montrer que f est injective ⇔ ∀ A ∈ P(E), A ⊂ f^(−1) (f(A))

$${Soit}\:{f}:\:{E}\rightarrow{F}\:,\:{une}\:{application}. \\ $$$$\mathscr{P}\left({E}\right)\:{est}\:{l}'{ensemble}\:{des}\:{parties} \\ $$$${de}\:{E}. \\ $$$${Montrer}\:{que}\:{f}\:{est}\:{injective}\:\Leftrightarrow\:\forall\:{A}\:\in\:\mathscr{P}\left({E}\right),\:{A}\:\subset\:{f}^{−\mathrm{1}} \left({f}\left({A}\right)\right) \\ $$

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Soit-f-E-F-une-application-P-E-est-l-ensemble-des-parties-de-E-Montrer-que-f-est-injective-A-P-E-A-f-1-f-A-

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