Question

and
are the two binary
operations defined for lattices.
O Join, meet
O Addition, subtraction
O Union, intersection
O Multiplication, modulo division​

Answer 1

Explanation:

Let L be a non-empty set closed under two binary operations called meet and join, denoted by ∧ and ∨. Then L is called a lattice if the following axioms hold where a, b, c are elements in L:

1) Commutative Law: -

(a) a ∧ b = b ∧ a (b) a ∨ b = b ∨ a

2) Associative Law:-

(a) (a ∧ b)∧ c = a ∧(b∧ c) (b) (a ∨ b) ∨ c = a ∨ (b ∨ c)

3) Absorption Law: -

(a) a ∧ ( a ∨ b) = a (b) a ∨ ( a ∧ b) = a

Duality:

The dual of any statement in a lattice (L,∧ ,∨ ) is defined to be a statement that is obtained by interchanging ∧ an ∨.

For example, the dual of a ∧ (b ∨ a) = a ∨ a is a ∨ (b ∧ a )= a ∧ a