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**1. Homework Statement**

Suppose that we partition R^3 into horizontal planes. What equivalence relation is associated with this partition? Suppose that we partition R^3 into concentric spheres, centered at (0,0,0). What equivalence relation is associated with this partition?

**2. Homework Equations**

**3. The Attempt at a Solution**

Since it is on R^3, I know that I need to come up with a partition that has an x, y and z coordinate, right?

Could the equivalence relation be (x,y,z)~(a,b,c) if and only if x^2=a^2?

For the second one, could it be something like (x,y,z)~(0,0,0) if and only if x^2=a^2

Thank you very much