Discrete Mathematics Answers

Draw the Hasse diagram of lattices, (L1,<) and (L2,<) where L1 = {1, 2, 3, 4, 6, 12} and L2 = {2, 3, 6, 12, 24} and a < b if and only if a divides b.

Let P be the power set of {a, b, c}. Draw the diagram of the partial order induced on P by the lattice (P,(,().

Show that p ⋁ (q ⋀ r) and (p ⋁ r) ∧ (p ⋁ r) are logically equivalent. This

is the distributive law of disjunction over conjunction.

Define a lattice. Explain its properties.

What is a partial order relation? Let S = { x,y,z} and consider the power set P(S) with relation R given by set inclusion. Is R a partial order

 Draw the Hasse diagram of lattices, (L₁,<) and (L₂,<) where L₁ = {1, 2, 3, 4, 6, 12} and

L₂ = {2, 3, 6, 12, 24} and a < b if and only if a divides b. 

Let A = {1,2,3,4} and let R = {(1,1), (1,2),(2,1),(2,2),(3,4),(4,3), (3,3), (4,4)} be an equivalence relation on R.  Determine A/R. 

Let X = {1,2,3,4,5,6,7} and R = {x,y/x–y is divisible by 3} in x. Show that R is an equivalence relation. 

Define the dual of a statement in a lattice L. why does the principle apply to L.

Let L be a lattice. Then prove that a Ù b=a if and only if a v b=b.