True and False? Let A and B be nonempty sets and f:->B be a function. Then if f(X∩Y)=f(X)∩f(Y) for all nonempty subsets X and Y of A, then f must be 1−1

mriteyl

mriteyl

Answered question

2022-10-08

True and False?
Let A and B be nonempty sets and f : A B be a function. Then if f ( X Y ) = f ( X ) f ( Y ) for all nonempty subsets X and Y of A, then f must be 1 1.

Answer & Explanation

Abigayle Lynn

Abigayle Lynn

Beginner2022-10-09Added 12 answers

True. If f were non-injective, two distinct elements of A would have the same image; taking their singleton sets then contradicts the hypothesis.

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