Syllogism — Monkeys, singing, and talking: Statement: • No monkey can sing, but some monkeys can talk. Which option states the correct logical consequence of the statement?

Introduction / Context:
The problem checks understanding of universal negative statements (“No A are B”) and particular affirmative statements (“Some A are C”). We must choose the option that must be true, not one that merely sounds plausible.

Given Data / Assumptions:

• No monkey can sing (Monkey ∩ Singer = ∅).
• Some monkeys can talk (∃ Monkey that are Talkers).
• Read “All monkeys can’t sing” as “No monkeys can sing.”

Concept / Approach:
Translate the English into set relations: the first clause is a universal exclusion, the second asserts existence of talkers among monkeys. Evaluate each option against these relations.

Step-by-Step Solution:
1) From “No monkey can sing,” it necessarily follows that no member of the Monkey set is in the Singer set.2) From “Some monkeys can talk,” at least one monkey is a Talker, but nothing is implied about all monkeys talking.3) (a) “Some monkeys may sing” contradicts the universal exclusion, so it is false.4) (b) “All monkeys can’t sing” restates the universal exclusion and must be true.5) (c) and (d) overgeneralize beyond the “some can talk” clause.

Verification / Alternative check:
A model with 10 monkeys, none singing, two talking, satisfies the statement and validates only option (b).

Why Other Options Are Wrong:
(a) contradicts the premise; (c) and (d) are not entailed.

Common Pitfalls:
Misreading “some” as “all,” or interpreting “can’t” ambiguously.

Final Answer:
All monkeys can't sing.