Direct Image of Intersection of Sets under an Injective Function Proof

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Direct Image of Intersection of Sets under an Injective Function Proof. Give an injective function f from X to Y and two subsets A, B of X, this video proves that the direct image of the intersection is the intersection of the direct images; i.e., f(A n B) = f(A) n f(B).
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thanks man... I watch all preimage and direct image videos .... helped a lot... thanks once again

krishnasingh
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Thanks man, super clear, highly appreciated. One question, what if the f is not injective?

rikyikhwan
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Wait so does this work for every function or only injective functions?

reinhardwilmer
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bro you just help me with part a of my problem which says, Let f : A→B be a mapping. a) Prove that if f is injective then f(C∩D)=f(C)∩f(D) for all the subsets C, D of A. b) Prove that f is injective if and only if for each subset C of A f(C)∩f(A-C)=∅. can you help me how i can approach b)

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