Question:hard

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?

Show 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.
Updated On: Jul 13, 2026
  • No Desdemonas are Belissimas.
  • Some Belissimas are Desdemonas.
  • Some Firdauses are both Belissimas and Cassandras.
  • Some Queens are neither Belissimas nor Elissimas.
Show Solution

The Correct Option is A

Solution and Explanation

A quicker route here is to first pin down one fact for certain: some Cassandras are Belissimas. We know all Alessandras are Belissimas, and we are told some Cassandras are Alessandras. Those particular Cassandras, being Alessandras, are automatically Belissimas too. So 'some Cassandras are Belissimas' is locked in as true.

Now check each option against the full picture:

  1. No Desdemonas are Belissimas: Desdemona's only ban is against being Alessandra, nothing bans it from Belissima. Since the Cassandra-Belissima overlap we just proved is not limited to only the Alessandra part, Desdemona can and does share part of that overlap. So claiming there is no overlap at all is wrong.
  2. Some Belissimas are Desdemonas: This is just the positive version of the same overlap, and it holds.
  3. Some Firdauses are both Belissimas and Cassandras: A Firdaus inside Belissima must be an Alessandra, from the earlier clue, and Alessandra overlaps Cassandra, so such a Firdaus is Belissima and Cassandra together. Holds.
  4. Some Queens are neither Belissimas nor Elissimas: The clues directly state some Cassandras sit outside Belissima, and those Cassandras cannot be Elissimas either, since Elissima needs staying out of Cassandra too. Holds.

Three of the four options check out under the diagram, only the blanket 'no overlap' claim in option (1) breaks down.

Let's summarize:

  • 'Some Cassandras are Belissimas' is a locked-in fact once you combine 'all Alessandras are Belissimas' with 'some Cassandras are Alessandras'.
  • Desdemona is never barred from Belissima, only from Alessandra, so it can share that overlap.

So the statement that is not true is option (1), 'No Desdemonas are Belissimas'.

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