Step 1: Understand what the question is asking.
We need to evaluate both the Assertion (A) and the Reason (R) about stock exchanges, then decide the correct relationship between them.
Step 2: Evaluate Assertion (A).
Assertion (A) states that the investing public gets a safe and fair deal on the stock market. This is absolutely correct. One of the recognized functions of a stock exchange is to provide safety and security to investors through regulated trading.
Step 3: Evaluate Reason (R).
Reason (R) states that membership is well regulated and dealings are well defined by the existing legal framework. This is also completely correct. Stock exchanges have strict admission criteria for brokers and all transactions must follow rules set by regulatory bodies like SEBI.
Step 4: Check whether Reason explains Assertion.
The reason the public can trust the stock market for safety and fairness is precisely because the members (brokers) operate under strict regulatory and legal controls. The regulation described in (R) is the direct cause of the safety described in (A).
Step 5: Compare with all four options.
Option (A) says both are correct and (R) is the correct explanation of (A). This fits perfectly. Options (B), (C), and (D) either deny the explanation link or deny the truth of one statement, which is not the case here.
Step 6: Arrive at the conclusion.
Since both statements are factually true and the Reason directly explains the mechanism behind the Assertion, the correct choice is Option (A).
\[ \boxed{ \text{Both (A) and (R) are correct; (R) correctly explains (A)} } \]