[" Q11.Let "A={x in Z:0<=x<=12}" .Show that "],[R={(a,b):a,b in A,|a-b|" is divisible by "4}" is an "],[" equivalence relation.Find the set of all elements "],[" related to "1." Also write the equivalence class "[2]" ."]

Corner points of the feasible region determined by the system of linear constraints are (0,3), (1,1) and (3,0). Let Z=px+qy , where p,q>0 . Find the condition in p and q, so that the minimum of Z occurs at (3,0) and (1,1).

The vertices of the feasible region determined by some linear constraints are (0,2), (1,1),(3,3), (1,5) . Let Z=px + qy where p,q gt 0 . The condition on p and q so that the maximum of Z occurs at both the points (3, 3) and (1, 5) is .......

Let f(x)= {(1, x in Q), (0, x in R-Q):} and g(x)= {(1, x in R-Q), (0, x in Q):} , find (f+g)(x) and (fg)(x).

Corner poins of the feasible region determned by the system of linear constrainsts are (0,3), (1,1), and (3,0). Let Z=px+qy. Where p, q lt 0 Condition on p and q, so that the minimum of Z occurs at (3,0) and (1,1) is

Corner poins of the feasible region determned by the system of linear constrainsts are (0,3), (1,1), and (3,0). Let Z=px+qy. Where p, q lt 0 Condition on p and q, so that the minimum of Z occurs at (3,0) and (1,1) is

Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).