Given an incumbent solution xin and the solution xlp of the LP relaxation at some node of the branch and bound tree. Under what conditions the branch at that node can be fathomed?(True or False) (a)...

Given an incumbent solution xin and the solution xlp of the LP relaxation at some node of the branch and bound tree. Under what conditions the branch at that node can be fathomed?(True or False)
(a) The objective function has an integer value at xlp;
(b) The gap between the two objective function values at xin and xlp is less than 1;
(c) The solution from the LP relaxation ( xlp ) is integer;
(d) The LP relaxation itself is infeasible.