(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let U be the set of all functions having R as domain and range a subset of R:

A={f|f is continous at each x ∈ R}

B={f|f is differentiable at each x ∈ R}

C={f|f '(x) = 2x + 3 for each x ∈ R}

D={f|f is a quadratic polynomial}

E={f|f(0) = 0}

F={f|f is a linear polynomial}

List all subset relationships between pairs of these 6 sets.

2. Relevant equations

A is a subset of B when every element of A is also and element of B.

3. The attempt at a solution

I'm having a hard time visualizing all these sets and being able to compare their elements. One thing I know from calc: If f is differentiable; then f is continuous. However, if f is continuous, it doesnt mean that f is necessarily differentiable. So I'm assuming A ⊆ B or B ⊆ A, I just don't know which way it is.

I also know that every set is a subset of itself.

So those are probally the easy answers, I'm having trouble relating the rest of them. If anyone could help me out, that would be great.

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# Homework Help: Subset Realtionship

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