regarding distributions of two random variables

There's a homework problem in my text that asks me to select an (odd) integer randomly from the set {1,3,5,7} and call it X. Then select an integer randomly from the set {0,1,2,3,4} add it to X. and then let Y be this sum.

(a) how can you show the joint p.m.f. of X and Y on the sample space of X and Y? I have drawn a table and labeled the axis accordingly, and matched up each sum and computed the sum at their intersection?

(b) How could one compute the marginal p.m.f.’s?

(c) and are X and Y independent? Reasons? I wrote yes but I'm not sure why.

Any help is appreciated thank you very much.