## Question

###### Problem 3 We let f:X _ Y be a function, prove that f is injective if and only if f(An B) = f(A) n f(B) for all A,B = X. (@Hint: To prove = (i.e: f(An B) = f(A) n f(B) implies f is injective) part, you can consider "proof by contradiction" and derive a contradiction by considering suitable choices of Aand B):

Problem 3 We let f:X _ Y be a function, prove that f is injective if and only if f(An B) = f(A) n f(B) for all A,B = X. (@Hint: To prove = (i.e: f(An B) = f(A) n f(B) implies f is injective) part, you can consider "proof by contradiction" and derive a contradiction by considering suitable choices of Aand B):

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