# Let f : A → B be a function and E, F are subsets of A. Show thatf (E ∪ F ) = f (E) ∪ f (F ) and f (E ∩ F ) ⊂ f (E) ∩ f (F )

## Question

## Solution 1

Sure, let's go through this step by step.

- f(E ∪ F) = f(E) ∪ f(F)

Proof:

Let's take an element y in f(E ∪ F). This means there exists an element x in E ∪ F such that f(x) = y. Now, x being in E ∪ F means that x is in E or x is in F. If x is in E, then y is in f(E). If x is in F, then y is in f( Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

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