Step-by-Step Logical Deduction

We can determine the profession of E by systematically processing the information provided.

1. Information from Initial Clues

First, let's establish the known facts from the main statements:

• Clue 1: "Lawyer A is married to D, Who is a housewife."
  • Person A's profession is Lawyer.
  • Person D's profession is Housewife.
  • (A, D) is one of the married couples.
• Clue 2: "C, the accountant is married to F, Who is a lecturer."
  • Person C's profession is Accountant.
  • Person F's profession is Lecturer.
  • (C, F) is the second married couple.
• Clue 3: "No lady is either an architect or an accountant."
  • This implies that the Accountant (C) and the Architect must be male.

2. Identifying Remaining People and Professions

Based on the above, we have assigned professions to A, C, D, and F. The people remaining are B and E.

The professions used are Lawyer, Housewife (one of two), Accountant, and Lecturer. The professions remaining are Architect and the second Housewife.

3. Applying the Final Condition

The question includes the condition: "If E is not a house wife".

We need to assign the two remaining professions (Architect, Housewife) to the two remaining people (B, E). If E is not a Housewife, then E must be assigned the only other available profession.

Conclusion

Given that E is not a Housewife, E's profession must be Architect.