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Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by

$$f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$$ Then $f(x, A \cup B)$ equals

  1. $f(x,A)+f(x,B)$
  2. $f(x,A)+f(x,B)\: – 1$
  3. $f(x,A)+f(x,B)\: – f(x,A) \cdot f(x,B)$
  4. $f(x,A)\:+ \mid f(x,A)\: – f(x,B) \mid $
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