Step 1: Formation of Grignard reagent.
The alkyl halide reacts with Mg in dry ether to form Grignard reagent:
\[
R–Br + Mg \xrightarrow{\text{ether}} R–MgBr
\]
Step 2: React Grignard with alcohol.
Grignard reagents react with alcohols to form alkanes:
\[
R–MgBr + CH_3OH \rightarrow R–H + CH_3OMgBr
\]
Step 3: Mechanism overview.
The acidic proton of CH\(_3\)OH protonates the carbanion of R–MgBr to yield R–H.
Step 4: Identify the product.
The major product is the hydrocarbon corresponding to R, here represented as R–CH\(_3\) after methyl group from CH\(_3\)OH.
Step 5: Verify alternative products.
R–OH is not formed because Grignard reacts with alcohol to give alkane, not alcohol. Other options involve different functional groups.