Discrete mathematics and lattice

Question

If X and Y are lattices then how to show that their cartesian product is also a lattice?I know that X and Y have sup. and inf. but how can I show their existance in cartesian product of X and Y?

Answer 1

You cannot show X×Y is a lattice.
You have to construct a lattice out of the other two lattices.
As a first step define (a,b) inf (x,y) as (a inf x, b inf y).