On the set A = {a, b, c}, where a, b, c are pairwise distinct, consider the relation R = {(a,a), (b,b), (c,c), (a,c)}.
List all the maximal and minimal elements of this partial order.
How would I answer this question? I know that the answer is:
Maximal elements = b, c
Minimal elements = a, b
But I don't know why. What makes those maximal and minimal elements?
Thanks.
List all the maximal and minimal elements of this partial order.
How would I answer this question? I know that the answer is:
Maximal elements = b, c
Minimal elements = a, b
But I don't know why. What makes those maximal and minimal elements?
Thanks.
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Aside from the reflexive relations, all you know is that a≤c so a is not maximal. That leaves b and c.
Similarly, you know that c is not minimal and that leaves a and b.
Similarly, you know that c is not minimal and that leaves a and b.