The purpose of the Business Case theme in PRINCE2is to establish a viable investment proposition. It justifies the investment in the project through an ongoing assessment of benefits, costs, and risks, ensuring that the project remains desirable, viable, and achievable throughout its life.References: PRINCE27 Foundation Source: PRINCE2Foundation handbook and online resources

The Progress theme provides all management levels within the project management team with mechanisms for monitoring and control. This theme ensures that there are clear benchmarks for performance and mechanisms in place to assess progress throughout the project's life cycle. References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.

The Project Board must review the Project Brief to confirm there is enough information to initiate the project.
The Project Brief includes the outline Business Case, the project's objectives, and how the project fits into the organization's objectives. This document is essential for the Project Board to understand what the project is intended to achieve, ensuring alignment with organizational goals and confirming that the project remains viable before moving forward into the initiation stage. References: PRINCE2 Foundation training manual and official handbook.

Both statements about the Project Initiation Documentation (PID) are correct. The PID is essential for establishing a solid foundation for the project, ensuring that all stakeholders agree on the project's objectives and how it will be managed before the Project Board authorizes it. Additionally, the PID should be updated at the end of each stage to reflect the current status of the project, ensuring that it continues to meet the project's requirements and objectives. References: PRINCE2 Foundation official documentation and study materials.

According to the PRINCE2 methodology, a key requirement for applying the organization theme is ensuring that each member of the project management team has a clear and written role description. This document outlines their duties, responsibilities, and relationships to other roles within the project, which is fundamental for organizational clarity and accountability. References: PRINCE2 7 Foundation Handbook and official training materials.