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Set Theoryhard
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Let f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R be a function and A,B⊆RA, B \subseteq \mathbb{R}A,B⊆R. Consider the sets SA={(x,y)∈R2:y=f(x),x∈A}S_A = \{ (x, y) \in \mathbb{R}^2 : y = f(x), x \in A \}SA​={(x,y)∈R2:y=f(x),x∈A} and SB={(x,y)∈R2:y=f(x),x∈B}S_B = \{ (x, y) \in \mathbb{R}^2 : y = f(x), x \in B \}SB​={(x,y)∈R2:y=f(x),x∈B}. Which of the following statements is always true?