# Discrete Mathematics-Properties of Lattices

Order Relations and Structures

Properties of Lattices

Theorem

Let L be a Lattice. Then for every a and b in L

(a) a V b = b if and only if a <, or = b

(b) a Λ b = a if and only if a <, or = b

(c) a Λ b = a if and only if a V b = b

#### Solution Summary

This solution is comprised of a detailed explanation for the Properties of Lattices.

It contains step-by-step explanation to show that if L is a Lattice, then for every a and b in L

(a) a V b = b if and only if a <, or = b

(b) a Λ b = a if and only if a <, or = b

(c) a Λ b = a if and only if a V b = b.

Solution contains detailed step-by-step explanation.