Step 1: Jack-up rigs.
Jack-up rigs are mobile platforms with extendable legs that can be lowered to the seabed. Once in place, the platform is jacked above sea level for stable drilling. Hence, they definitely have legs resting on the seabed.
Step 2: Tension leg platforms.
Tension leg platforms are floating structures tethered to the seabed by vertical tensioned tendons or tethers. These are not "legs resting on seabed" but mooring elements providing vertical stability. Hence, option (B) is incorrect.
Step 3: Concrete gravity platforms.
Concrete gravity-based structures (GBS) rest directly on the seabed. Their enormous weight (gravity base) provides stability. They have large "legs/shafts" rising above the seabed. Hence, (C) is correct.
Step 4: Semi-submersibles.
Semi-submersibles float on partially submerged pontoons and are held in place by anchors or dynamic positioning systems. They do not have legs resting on the seabed. Thus, (D) is incorrect.
Final Answer:
\[
\boxed{\text{(A) Jack up and (C) Concrete gravity platforms}}
\]