I understand this isn't a homework area but there is always so much more traffic in this forum rather than the homework. All I'm looking for is a clarification that my ideas to prove both parts are in fact accurate.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

If each of D1 and D2 is a subdivision of [a,b], then...

1. D1 u D2 is a subdivision of [a,b], and

2. D1 u D2 is a refinement of D1.

2. Relevant equations

**Definition 1: The statement that D is a subdivision of the interval [a,b] means...

1. D is a finite subset of [a,b], and

2. each of a and b belongs to D.

**Definition 2: The statement that K is a refinement of the subdivision D means...

1. K is a subdivision of [a,b], and

2. D is a subset of K.

3. The attempt at a solution

My problem is that I've taken a lot of logic courses in the past so when I see the union of two variables I only need to prove that one is actually true. In this particular situation both are true so its obvious but I don't know how to state that fact.

For the 2nd part of the proof, wouldn't I just say that D1 is a subset of itself, and its already given that D1 is a subdivision of [a,b]? It just seems too easy...

I also had questions about proofs I've already turned in that I did poorly on but I didn't want to flood this place with questions.

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# Subdivisions/Refinement Proof

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