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

Picture this as a Venn diagram inside one big circle, Queen. Draw Belissima and Cassandra as two overlapping circles inside Queen, and mark the region outside both of them as Elissima, because the last clue tells us Elissima is exactly ‘Queen but not Belissima and not Cassandra’. Alessandra sits fully inside Belissima, since every Alessandra is a Belissima.

Now bring in Firdaus. The third clue says a Belissima who is not an Alessandra cannot be a Firdaus. In other words, the part of the Belissima circle that lies outside Alessandra is completely closed off to Firdaus. So wherever a Firdaus lands inside Belissima, it must land inside the smaller Alessandra circle.

Think about the whole Queen circle as three zones for any Firdaus: inside Belissima (which, as just shown, forces it into Alessandra), inside Cassandra but outside Belissima, or outside both Belissima and Cassandra (which is the Elissima zone). There is no fourth zone left in the diagram, because these three zones are drawn to cover the entire Queen circle between them.

So a Firdaus can only ever fall in one of three places: the Alessandra zone, the Cassandra-only zone, or the Elissima zone. That is exactly option (3): all Firdauses are either Alessandras, Cassandras, or Elissimas.

Let's summarize:

• Firdaus is barred from the ‘Belissima but not Alessandra’ strip of the diagram.
• Every remaining zone of the diagram is labelled Alessandra, Cassandra, or Elissima.
• The other three options only claim what might be true for a Firdaus, not what must be true.

So the statement that always holds is option (3), all Firdauses are either Alessandras, Cassandras or Elissimas.