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 not true?

• A. No Desdemonas are Belissimas.
• B. Some Belissimas are Desdemonas.
• C. Some Firdauses are both Belissimas and Cassandras.
• D. Some Queens are neither Belissimas nor Elissimas.

Hint:

First lock down that some Cassandras are Belissimas, using the Alessandra overlap, then check that nothing in the clues stops Desdemona from sharing that same overlap.

Answer 1

The Correct Option is A

Step 1: Recall the diagram from the previous question.
Alessandra sits inside Belissima. Some Cassandras are Alessandras, so that overlap sits inside the Belissima-Cassandra overlap too, since Alessandra is inside Belissima. Also, some Cassandras are not Belissimas at all, so the Cassandra circle sticks out beyond Belissima.

Step 2: Place Desdemona.
Every Desdemona is a Cassandra, and no Desdemona is an Alessandra. So Desdemona sits inside the Cassandra circle, in the part that avoids Alessandra. Nothing in the clues stops that part of Desdemona from dipping into the Belissima-Cassandra overlap, the clues only ever exclude Alessandra for Desdemona, never Belissima. So the diagram places some Desdemonas inside Belissima, through the Cassandra-Belissima overlap, and some outside it.

Step 3: Test option (1) and (2).
Because some Desdemonas do sit inside the Belissima-Cassandra overlap, ‘No Desdemonas are Belissimas’ does not hold, so option (1) is not true, it is contradicted by the diagram.
Its flip side, ‘Some Belissimas are Desdemonas’, correctly describes that overlap, so option (2) does hold.

Step 4: Test option (3) and (4).
From the previous question, a Firdaus that sits inside Belissima must also sit inside Alessandra, and Alessandra overlaps Cassandra. So the Firdauses that land in that Alessandra part are both Belissimas and Cassandras at once, which makes option (3) true.
Since some Cassandras lie outside Belissima (given directly in the clues), those Queens are Cassandras but not Belissimas, and being outside Belissima and inside Cassandra keeps them out of the Elissima zone too, since Elissima needs staying outside both. So they are Queens that are neither Belissima nor Elissima, which makes option (4) true.

Final Answer:
Only option (1) fails to hold, so it is the one that is not true. \[ \boxed{\text{Option 1}} \]