Question

Which is a valid assignment?

• A. A-Home, B-Power, C-Defence, D-Telecom, E-Finance.
• B. C-Home, D-Power, A-Defence, B-Telecom, E-Finance.
• C. A-Home, B-Power, E-Defence, D-Telecom, F-Finance.
• D. B-Home, F-Power, E-Defence, C-Telecom, A-Finance.
• A. D-Defence, B-Telecom.
• B. F-Defence, B-Telecom.
• C. B-Defence, E-Telecom.
• D. B-Defence, D-Telecom.

Answer 1

The Correct Option is B

Step 1: Write the four conditions in a testable form:
Five of the six people get one portfolio each, and one person stays out. The conditions are:
(i) If D gets a portfolio, F gets none, so D and F can never both appear.
(ii) C can hold only Home or Finance. Otherwise C must stay out.
(iii) If D holds Power, then B holds Telecom. If D holds Telecom, then B holds Power.
(iv) If A holds a portfolio, E must hold one too.

Step 2: Check option (1):
A-Home, B-Power, C-Defence, D-Telecom, E-Finance.
Here C holds Defence, but C is allowed only Home or Finance. Condition (ii) fails, so (1) is invalid.

Step 3: Check option (2):
C-Home, D-Power, A-Defence, B-Telecom, E-Finance.
(i) F is the person left out, so D and F are not together. This holds.
(ii) C holds Home, which is allowed.
(iii) D holds Power and B holds Telecom, exactly the pairing B asked for.
(iv) A holds Defence and E holds Finance, so E has a portfolio.
All four conditions hold. So (2) is valid.

Step 4: Check option (3):
A-Home, B-Power, E-Defence, D-Telecom, F-Finance.
D and F both hold portfolios, which breaks condition (i). So (3) is invalid.

Step 5: Check option (4):
B-Home, F-Power, E-Defence, C-Telecom, A-Finance.
C holds Telecom, which breaks condition (ii). So (4) is invalid.

Final Answer:
Only option (2) satisfies every condition. \[ \boxed{\text{Option 2}} \]

Answer 2

Step 1: Fix what is given and what follows from it:
A has Home and C has Finance. Since A holds a portfolio, E must also hold one (E insists on a portfolio if A gets one). So A, C and E are in.
Five people must be appointed, so exactly two more come from B, D and F. D and F cannot both be in, because F does not want a portfolio if D gets one.
So the two extra people are either B and D, or B and F. In both cases B is in, and exactly one of D, F is in.

Step 2: The three portfolios left:
Power, Defence and Telecom are left for E, B and one of D or F. We need the option that cannot be completed in a valid way.

Step 3: Check option (1): D-Defence, B-Telecom:
E must take Power. So A-Home, C-Finance, D-Defence, B-Telecom, E-Power, with F out.
D holds Defence, so B's rule about Power or Telecom is not triggered. F is out as required. This is valid.

Step 4: Check option (2): F-Defence, B-Telecom:
E must take Power. So A-Home, C-Finance, F-Defence, B-Telecom, E-Power, with D out.
D is out, so F may be in. Nothing is broken. This is valid.

Step 5: Check option (3): B-Defence, E-Telecom:
Power goes to D or F. If D took Power, B would have to take Telecom, but E has it, so that fails. If F takes Power, then D is out and everything is fine: A-Home, C-Finance, B-Defence, E-Telecom, F-Power.
One valid completion exists, so this option can be a valid assignment.

Step 6: Check option (4): B-Defence, D-Telecom:
D holds Telecom, so B must hold Power. But B already holds Defence, so B cannot hold Power. B's condition is broken.
Changing the remaining slot does not help, because the problem is already in the two portfolios given. So this assignment can never be valid.

Final Answer:
Option (4) is the one that is NOT a valid assignment. \[ \boxed{\text{Option 4}} \]