Statement 1 is correct: The Speaker of the Legislative Assembly shall vacate their office if they cease to be a member of the Assembly. This is explicitly provided under Article 179 of the Indian Constitution. Statement 2 is incorrect: It is incorrect to say that the Speaker vacates office immediately upon the dissolution of the Legislative Assembly. When the Assembly is dissolved, the Speaker does not vacate office immediately. Instead, the Speaker continues in office until the newly elected Assembly convenes for the first time and elects a new Speaker. This ensures continuity in the legislative process and prevents a vacuum in constitutional functions. So, only the first statement is correct.