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Directions
For this assignment, you will need to prove (or disprove) the following statements. You will also need to record yourself presenting the proof of each. You can do this as three videos or just one. You can record these on Zoom (or Google meet) and provide a link similar to how I do for our videos for this class (recording to a cloud). Pictures of the proofs and link(s) to your videos is what you will submit!
Your video should include the following:
A brief introduction where you show your face and introduce yourself.
A statement of the problem you are solving.
A step by step explanation of what you did to prove this statement.
A clear ending to a proof( Since the Question is asking for a video, I will need a detailed script to read from for my own purposes explaining each question on the homework)
Questions
1. Given f: A → B and subsets Y, Z C B, prove the relation below:
f-‘(Ynz) =f-‘(Y)nf-‘(z)
2. Consider the function f : R? → R? defined by the formula f(x, y) = (zy, x3). Find a formula for fo f (Nothing to prove here, just show the calculation and the steps).
3. Define a relation R on Z as xRy if and only if z? + y? is even. Prove R is an equivalence relation.
Describe its equivalence classes.

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