Proving a partial order and total order. - In each of the following say whether or not R is a partial order on A. If so, is it a total order?
a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)}
b) A is the set of positive divisors of 24, ...
Finite proof - Let R ba a partial order on S, and suppose that x is a unique minimal element in S.
a) prove that S is finite, then xRy for all s in S
b) show that the conclusion in (a) need not be true if S is inf ...
Working with partial order relations in discrete math. - Let S = {0,1} and consider the partial order relation R defined on S X S X S as follows: for all ordered triples (a, b, c) and (d, e, f) in S X S X S.
( a, b, c ) R ( d, e, f ) <-> a ≤ ...
Partial derivative - Compute the first-order partial derivative of the given function
z=xy^2/x^2y^3+1