3.A function fR R is defined as follows:

f(x)=3x/(x^2+1)

1. Determine the result area set / function image
2. Is this function an injective and surjective function? Tell

4. A relation R on the set Z Z is defined by:

(m,n) R(p,q) if and only if m+q=n+p

a. Show that R is an equivalence relation and explain the equivalence classes of (1,1), (2,1), (3,1), (1,2) and (1,3).

b. For example A={0,1,2} {2,5,8}

= {(0,2), (0,5), (0,8), (1,2), (1,5), (1,8), (2,2), (2,5), (2.8)}.

The partially ordered relation (Poset) R on A is defined by:

(a,b) R(c,d) if and only if (a+b) is divisor (c+d)

(i). Draw a Hasse diagram for poset A

(ii). Determine the maximum, minimum, maximum, and minimum elements (if any) in poset A.

(iii). Determine LB (0.8) and GLB (0.8).

(LB = Lower Bound, GLB = Greates Lower Bound)