I am stuck on the below problem. My answers are in bold. I need help with the transfer functions and defintion of the latice. As well as the proof that it is monotone or distributive. Thank you

The intraprocedural Must-be-modified problem is a backward dataflow problem solvable by fixpoint iteration. A variable is in the must-be-modified set on exit of CFG node n, if it is modified on all paths from n to exit. The problem statement is as follows: for each node n compute the set of variables that are in the must-be-modified set on exit from n.

a) (5 pts) Define the analysis as an instance of the dataflow framework.

Specify Lattice L, : D is the set of all expressions in the program. is superset and join of the lattice is set intersection as needed for a must problem.

Merge operator: The merge operator is the join of L and thus is set intersection.

Transfer functions:

b) (5 pts) Are the functions for this problem distributive or monotone? Show your proof

Monotone because the functions are actually distributive and therefore monotone.