Directions: Analyze the given statements and select the conclusion that logically follows.

Statements:
1. All architects are designers.
2. Some designers are painters.

Which of the following must be true?

The correct answer is Some designers are architects.

Step-by-Step Explanation:

Step 1: Analyze Statement 1
Statement 1: "All architects are designers."
This is a universal affirmative statement. In standard categorical logic, if every architect is a designer, then at least those designers who are architects must exist within the set of designers. Therefore, by immediate inference (conversion of an 'A' type statement to an 'I' type statement), it logically follows that "Some designers are architects."

Step 2: Evaluate the given options
1. All designers are architects: Incorrect. The premise establishes that architects are a subset of designers, but not necessarily that designers are limited only to architects.
2. Some architects are painters: Incorrect. Statement 2 tells us that some designers are painters, but those painters might be outside the subset of architects.
3. Some designers are architects: Correct. As established in Step 1, this is a valid direct conclusion from Statement 1.
4. All painters are architects: Incorrect. There is no relationship given to support that all painters must be architects.

Thus, the conclusion that logically follows is Some designers are architects.