Step 1: Concept
$\beta$-lactam antibiotics target specific structural components unique to bacterial anatomy to kill bacterial cells without harming eukaryotic host structures.
Step 2: Meaning
Inhibiting synthesis means stopping the cross-linking of the protective peptidoglycan layer, leaving the bacterial cell vulnerable to osmotic pressure.
Step 3: Analysis
* Assertion (A) is correct: Penicillin is a classic, widely used bactericidal antibiotic prescribed to treat a variety of susceptible bacterial infections.
* Reason (R) is correct: Mechanistically, the $\beta$-lactam ring of penicillin binds to and inhibits transpeptidase enzymes (penicillin-binding proteins). This stops the cross-linking of peptidoglycan chains, weakening the cell wall until the bacterium bursts from osmotic lysis.
* Explanation assessment: The reason details the exact biochemical mechanism behind the therapeutic effect mentioned in the assertion, providing a direct explanation.
Step 4: Conclusion
Both statements are true, and (R) provides the logical mechanism that explains (A).
Final Answer: (A)