Step 1: Start by eliminating using coal bed methane: Coal bed methane gas is known to be held by adsorption on the coal surface rather than existing freely, so R must pair with I, gas mostly present in adsorbed state. Checking the four options, option B and option D pair R with IV instead of I, so both B and D can be ruled out immediately.
Step 2: Use gas hydrate to narrow further: Gas hydrates are well known clathrate compounds where gas molecules sit inside cages formed by water molecules, so P must pair with IV. Between the two remaining candidates, option A and option C, both correctly pair P with IV, so this step alone does not separate them.
Step 3: Use oil shale to separate the remaining options: Oil shale is defined as the parent sedimentary rock containing kerogen, so Q must pair with II, sedimentary rock contains kerogen. Option A instead pairs Q with III, oil recovered from shale, which actually describes shale oil, not oil shale, so option A is eliminated.
Step 4: Confirm with shale oil: Shale oil is the oil product recovered from oil shale, so S must pair with III. Option C pairs S with III, which is consistent with this reasoning.
Step 5: Final check of option C: Option C gives P-IV, Q-II, R-I, S-III, and every one of these four pairs has now been independently verified through the definitions of gas hydrate, oil shale, coal bed methane and shale oil, so option C is the only fully consistent choice.
Final Answer: $oxed{ ext{(C) P - IV; Q - II; R - I; S - III}}$