This is my calculus homework. Can you please help ASAP? Thank you.

Consider the statement R above and the following formal "proofs". Select all those which are correct.

Proof that R is true. Let x E R be arbitrary and take y = x - 1. Then if z > y, we have z>x. This proves R.

Proof that R is true. Let x E R be arbitrary and take y = x + 1. Then if z > y, we have z>x. This proves R.

Proof that R is false. Take x=0 and y=-2. Then taking z = - 1 we have z>y and z x. Thus R is false.

Proof that R is false. Take x=0 and let y E R be arbitrary. Then there exists zE R with 0 < z y, we have z>x. This proves S.