All architects are designers. Some designers are painters. No painters are accountants. Based strictly on these premises, which of the following conclusions must logically follow?

Answer and explanation

Correct answer: C. Some designers are not accountants.

  1. Step 1: Evaluate set relationships from premises:
  2. Step 2: Premise 2: Some designers are painters (there is a non-empty intersection between Designers and Painters).
  3. Step 3: Premise 3: No painters are accountants (Painters and Accountants are mutually disjoint sets).
  4. Step 4: Since those designers who are painters cannot be accountants, it must follow that some designers are not accountants.
  5. Step 5: Check other options: Nothing requires architects to be painters or prevents architects from being accountants outside the painter subset.
Answer
Some designers are not accountants.
Why not the others: 'All architects are painters' is unsupported as architects may be designers who do not paint; 'No architects are accountants' is invalid because architects could overlap with non-painter accountants; 'All painters are designers' commits the illicit conversion of 'some designers are painters'.

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