Hello,
F: a/c<b/c and c>0==>a/c*c<b/c*c==>a<b : FALSE
G: c/a<c/b and c>0==>1/a<1/b==>b<a
explanation:
if a<0 =>b<0 (since a*b>0) then
1/a<1/b==>b/a>1 ==>b<a ==> True
if a>0 then b>0 (since a*b>0) then
1/a<1/b==>b/a<1 ==>b<a ==>True
H: a-c<b-c==>a-c+c<b-c+c==>a<b ==> False
K: a+c<b-c==>a<b-2c < b ==>a<b (since c>0) False
