a. Let (A,<) be a strictly ordered set and b not in A. Define a relation in {b} as follows:
x y iff (x,y in A and x<y) or (x in A and y=b). Show that is a strict ordering of B and (Intuitively, keeps A ordered in the same way as < makes b greater than every element of A.)
b. Generalize part (a): Let ( ) and ( ) be strict orderings, . Define a relation on B = as follows:
x y iff x,y in and
or x,y in and
or x in and y in
Show that is a strict ordering of B and . (Intuitively, puts every element of before every element of and coincides with the original orderings of and
Does anyone have any suggestions on how to do this?