The product of two lattices is a lattice.
The previous exercise implies that the product of n lattices is a lattice, with ∨ and ∨ defined componentwise, that is,
x ∨ y = (x1 ∨ y1, x24y2; . . . ; xn ∨ yn)†
x ∧ y = x1 ∧ y1, x2 ∧ y2, . . . , xn ∧ yn)†