Assertion (A): When sodium carbonate is added to diluted hydrochloric acid, gas bubbles can be observed. 

Reason (R): During the process, carbon dioxide is released.

Sodium carbonate reacts with excess hydrochloric acid to form sodium chloride, water and carbon dioxide. In this reaction, bubbles of carbon dioxide are observed.  

$$N{a}_{2}C{O}_3 \left(s\right) + 2HCl\left(aq\right) \to 2NaCl\left(aq\right) + H_{2}O\left(l\right) + C{O}_2\left(g\right)$$

Hence, the correct option is (a) Both A and R are true, and R is the correct explanation of the assertion.