The correct option is "1 only." The Speaker of the Legislative Assembly indeed vacates his/her office if they cease to be a member of the assembly, as the position is inherently linked to membership. However, the second statement is incorrect because the Speaker does not vacate the office immediately upon the dissolution of the Legislative Assembly; they continue to hold the position until a new assembly is formed, ensuring continuity in the legislative process. This understanding is critical for comprehending the functions of legislative bodies in parliamentary democracy, a topic often explored in UPSC preparatory materials.