Discrete Mathematics Answers

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.

If a function is defined as f(x,n) mod n. Determine the

i.     Domain of f

ii.   Range of f

iii.   G(g(g(g(7)))) if g (n) = f(209, n).

Determine whether the following relations are injective and/or subjective function. Find universe of the  functions if they exist.

A = 1,2,3,4,5 B=1,2,3,4,5

           R = (1,2),(2,3),(3,4),(4,5),(5,1)

Determine whether the following relations are injective and/or subjective function. Find universe of the  functions if they exist.

i.     A= v,w,x,y,z, B=1,2,3,4,5

       R= (v,z),(w,1), (x,3),(y,5)