(A) CO₂ reacts with Grignard reagent followed by acid catalysed hydrolysis gives carboxylic acid. 
(R) Alkyl halide reacts with Mg in the presence of ether gives Grignard reagent.

Explanation of (A)

Grignard reagents (RMgX) react with carbon dioxide (CO₂) to form a magnesium carboxylate intermediate, which upon acid-catalysed hydrolysis gives a carboxylic acid. This is a well-known synthetic route in organic chemistry to prepare carboxylic acids with an additional carbon atom:

RMgX + CO₂ → RCOOMgX
RCOOMgX + H⁺/H₂O → RCOOH + Mg²⁺ + X^-

Explanation of (R)

Grignard reagents are prepared by reacting alkyl or aryl halides with magnesium in dry ether. The solvent ether stabilizes the Grignard reagent and prevents side reactions:

RX + Mg (in dry ether) → RMgX

Relationship Between (A) and (R)

Both statements (A) and (R) are correct. The reaction described in (R) produces the Grignard reagent needed for the reaction in (A). Therefore, (R) correctly explains the formation of the reagent that reacts with CO₂ to form the carboxylic acid.