Need Handwritten Solution with proper explanation for every part as soon as possible

1. (a) Prove, using only the axioms of set theory, that for every S there is an r such that I @ S. (b) Prove that for every S there is an infinite set T such that Sn T = 0. (c) Give an example of a finite set S, a partial order R on S and an element r of S which is a minimal element of S with respect to the order R but is not a least element. (d) Give two examples of a well-founded relation which is not a well ordering