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 is true?

• A. All Firdauses are Alessandras.
• B. Some Firdauses are Alessandras.
• C. All Firdauses are either Alessandras, Cassandras or Elissimas.
• D. Some Firdauses are Cassandras.

Hint:

Split every Firdaus by whether it is a Belissima, a Cassandra, or neither, then use the rule that a Belissima Firdaus must be an Alessandra along with the Elissima rule to see the only three possible zones.

Answer 1

The Correct Option is C

Step 1: Write the clues as set relations.
Use A, B, C, D, E, F for Alessandra, Belissima, Cassandra, Desdemona, Elissima, Firdaus, and Q for Queen.
The clues say A sits inside B, since every Alessandra is a Belissima. Every Firdaus that is also a Belissima must be an Alessandra (this is just the third clue restated). All six groups sit inside Q. And the key rule for Elissima is: a Queen is an Elissima exactly when it is neither a Belissima nor a Cassandra.

Step 2: Work out where a Firdaus can sit.
Take any Firdaus and call him x. Since every Firdaus is a Queen, x is a Queen.
Now split on whether x is a Belissima or a Cassandra.
Case 1: x is a Belissima. The clue on Firdaus says a Belissima who is a Firdaus must be an Alessandra, so x is an Alessandra.
Case 2: x is not a Belissima but is a Cassandra. Then x is simply a Cassandra.
Case 3: x is neither a Belissima nor a Cassandra. Since x is a Queen, the Elissima rule then forces x to be an Elissima.
These three cases cover every possibility for x, because ‘Belissima or not’ and ‘Cassandra or not’ between them exhaust all Queens.

Step 3: Check each option against this.
Option (1), ‘All Firdauses are Alessandras’, fails because Case 2 and Case 3 show a Firdaus can be a plain Cassandra or an Elissima instead.
Option (2), ‘Some Firdauses are Alessandras’, is not guaranteed, since the clues never force even one Firdaus to actually be an Alessandra, it is only a possibility, not a certainty.
Option (4), ‘Some Firdauses are Cassandras’, has the same problem, it is possible but not something the clues force to be true.
Option (3) exactly matches the three-way split found above, every Firdaus must be an Alessandra, a Cassandra, or an Elissima, with no other option left over.

Final Answer:
Option (3) is the statement that must be true. \[ \boxed{\text{Option 3}} \]