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Set Theoryhard
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Let SSS be the set of all continuous functions f:[0,1]→Rf: [0, 1] \to \mathbb{R}f:[0,1]→R. Consider two subsets of SSS: A={f∈S:f(x)≥0 for all x∈[0,1]}A = \{ f \in S : f(x) \ge 0 \text{ for all } x \in [0, 1] \}A={f∈S:f(x)≥0 for all x∈[0,1]} B={f∈S:∫01f(x)dx=0}B = \{ f \in S : \int_0^1 f(x) dx = 0 \}B={f∈S:∫01​f(x)dx=0} Which of the following statements about A∩BA \cap BA∩B is true?