Answer Happy

Question is in Picture. This is from Abstract Algebra: Modules.
Please answer if you are familiar with the topic and can answer in
a clear and detailed way. The textbook used is: Abstract Algebra -
3rd Edition by David S. Dummit, Richard M. Foote. Thank you!
1. An element m of the R-module M is called a torsion element if rm = 0 for some nonzero r E R. Moreover, Tor(M) = {m E M : rm = O for some nonzero r e R}. (a) Prove that if R is an integral domain, then Tor(M) is a submodule of M (called the “torsion" submodule of M). (b) Let o: M N be an R-module homomorphism. Prove that (Tor(M)) C Tor(N).