Step 1: Analyze boiling point factors.
Boiling point depends on intermolecular forces like hydrogen bonding, van der Waals forces, etc.
Step 2: Compare methoxymethane and ethanol.
Methoxymethane (CH$_3$–O–CH$_3$) is an ether and shows dipole-dipole interactions but no hydrogen bonding.
Ethanol (CH$_3$CH$_2$OH) has strong hydrogen bonding due to the –OH group.
Step 3: Result.
Hydrogen bonding increases boiling point. Hence, ethanol has a higher boiling point than methoxymethane.
So, statement A is false.