Step-by-Step Logical Deduction

To determine E's profession, we can use a process of elimination and a table to track the attributes of each person (A, B, C, D, E, F).

The Professions to be Assigned:

• Housewife (2)
• Professor (1)
• Engineer (1)
• Accountant (1)
• Lawyer (1)

Analyzing the Clues

1. "C, the accountant, is married to F, who is professor."
   • C's profession is Accountant.
   • F's profession is Professor.
   • (C, F) is one of the two married couples.
2. "No woman in the group is either an engineer or an accountant."
   • This means the Accountant (C) and the Engineer must be male. Since C is male, his wife F must be female.
3. "The lawyer is married to D, who is housewife." and "A is married to a housewife."
   • These clues together tell us that A must be the Lawyer and he is married to D, who is a Housewife.
   • This identifies the second couple (A, D). Since D is a housewife (female), A must be male.

Determining the Remaining Roles

At this point, we have assigned professions to A (Lawyer), C (Accountant), D (Housewife), and F (Professor). The people remaining are B and E.

The professions remaining are the second Housewife and the Engineer.

Applying the Final Clue

We need to assign the roles of Housewife (female) and Engineer (male) to B and E.

• The final clue states: "E is not a housewife."
• If E is not the Housewife, he must take the only other available role.

Conclusion

Therefore, E's profession must be Engineer.