Intersection Of Two Intervals

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Problem 20: (Intersection Of Two Intervals)

Suppose that $a,b,c,d\in \mathbb{R}$ and that $a<b<c<d$. Consider the intervals $ A=(a,c) $ and $ B=[b,d] $. Prove that $A\cap B = [b,c) $. (Remember this means you need to prove that $A\cap B \subseteq [b,c) $ and $ [b,c)\subseteq A\cap B$.

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