4. Let X = [0, 1] x [0,1]. Defineon X by (a, b)~ (c,d) if and only if either (1) (a, b) = (c,d)

or (2) a = c and {b,d} = {0,1}. The relation is an equivalence relation, and you can use

that fact in your reasoning for this problem.

(a) For each point of X provided, list all of the points in X that relate to it via ~. (None of

these lists are infinite or even very long.) i. (). (0,0) iii. (,0) iv. (1,1)

(b) Take a square piece of paper, label several points on it so that you can pretend the paper

represents X. Use tape to overlay the points that relate via~. What is the resulting

shape?