Need to prove all three statements relating to upper and lower bounds

Question

I had this proof for the first one: Assume that S is a nonempty subset of bounded below. Then there exists an x in S such that x is less than or equal to s for all s in S. Then, we can multiply both x and s by negative one and we get -s is less than or equal to -x for all s in set S. Thus, we can conclude the set -S denoted by {-s:for all s in S} is bounded above. But my professor stated that it would be incorrect and that i should start by choosing an arbitrary element in -S and using it to prove -S is bounded above. This image has all three proofs that need solving.