Question: For X = {0, 1}, let A = X X. Define the relation R on A by (a, b) R (c, d) if (i)

For X = {0, 1}, let A = X × X. Define the relation R on A by (a, b) R (c, d) if
(i) a < c; or
(ii) a = c and b ≤ d.
(a) Prove that R is a partial order for A.
(b) Determine all minimal and maximal elements for this partial order.
(c) Is there a least element? Is there a greatest element?
(d) Is this partial order a total order?

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