Question

Directions for questions 41 to 44: Ghosh Babu's new interest is psychology. He has identified various personality patterns and given them names. These personality patterns are inter-related as follows:
- All Alessandras, Belissimas, Cassandras, Desdemonas, Elissimas and Firdauses are Queens.
- All Alessandras are Belissimas.
- No Belissima that is not an Alessandra is a Firdaus.
- Some Cassandras are Alessandras.
- All Desdemonas are Cassandras.
- Some Cassandras are not Belissimas.
- No Desdemona is an Alessandra.
- All Queens and only Queens that are neither Belissimas nor Cassandras are Elissimas.

Which of the following cannot be said to be true or false?
I. No Belissima or Cassandra is an Elissima.
II. Some Cassandras are Belissimas but not Alessandras.
III. No Belissima is both an Alessandra and a Desdemona.

• A. I only
• B. II only
• C. III only
• D. I & II

Hint:

Statements I and III follow straight from the definitions and clues given, but statement II depends on a detail the passage never fixes, try building two valid pictures where it comes out differently.

Answer 1

The Correct Option is B

Step 1: Check statement I.
The last clue defines Elissima as exactly ‘a Queen that is neither a Belissima nor a Cassandra’. So by definition, nothing that is a Belissima or a Cassandra can be an Elissima. Statement I, ‘No Belissima or Cassandra is an Elissima’, matches this definition exactly, so it is definitely true. It can be judged.

Step 2: Check statement III.
One of the clues says directly that no Desdemona is an Alessandra, meaning the group ‘Alessandra and Desdemona together’ is empty. If that combined group is already empty, then a smaller group inside it, ‘Belissima and Alessandra and Desdemona together’, must also be empty. So ‘No Belissima is both an Alessandra and a Desdemona’ is definitely true. It too can be judged.

Step 3: Check statement II.
We know some Cassandras are Alessandras, so that overlap sits inside Belissima too, since Alessandra is inside Belissima, and we know some Cassandras are not Belissimas at all. But nothing in the clues says how big the plain ‘Cassandra and Belissima but not Alessandra’ slice is. It could be empty, if every Cassandra that is a Belissima happens to also be an Alessandra, or it could be non-empty, if some Cassandras are Belissimas for a reason other than being Alessandras. Both pictures fit every clue given. So we cannot say for sure whether statement II is true or false, it genuinely depends on details the passage never pins down.

Step 4: Conclude.
I and III are settled facts, forced by the clues. II is the one statement that stays undecided either way.

Final Answer:
Only statement II cannot be said to be true or false. \[ \boxed{\text{Option 2, II only}} \]