Let

P

and

Q

be sets with total orders

and

. The pre-order on the cross product is defined:\

(p,q)

\ Show, reflexivity, transitivity, and that it is anti-symmetric.

Let P and Q be sets with total orders P and Q. The pre-order on the cross product is defined: (p,q)pQ(p,q)EpppandqQq. Show, reflexivity, transitivity, and that it is anti-symmetric