Step 1: Understanding the Concept:
Heterocyclic compounds are ring compounds containing an atom other than carbon. Some are aromatic with C=C bonds in the ring, and some are saturated.
Step 2: Key Formula or Approach:
Recall the structure of each ring and count the double bonds.
Step 3: Detailed Explanation:
Tetrahydrofuran (THF) is \(\text{C}_4\text{H}_8\text{O}\), a five-membered ring of four \(\text{CH}_2\) groups and one oxygen. All bonds are single, so it has no double bond.
4H-Pyran is a six-membered ring with one oxygen and two C=C bonds, with one \(\text{CH}_2\) at position 4.
Pyrrole is a five-membered aromatic ring with nitrogen and two C=C bonds.
Thiophene is a five-membered aromatic ring with sulfur and two C=C bonds.
Final Answer:
Only tetrahydrofuran is fully saturated and has no double bond, option (A).
\[ \boxed{\text{Tetrahydrofuran (A)}} \]