Syllogism — From the statements below, identify the correct conclusion(s): Statements: I. Some keys are locks; some locks are numbers. II. All numbers are letters; all letters are words. Conclusions: I. Some words are numbers. II. Some locks are letters.

Introduction / Context:This problem combines particular and universal premises across five terms. We must check two candidate conclusions.

Given Data / Assumptions:

• Some keys are locks; some locks are numbers.
• All numbers are letters; all letters are words.

Concept / Approach:Use subset chaining for universals and existence from particulars. If Numbers ⊆ Letters ⊆ Words, then every Number is a Word.

Step-by-Step Solution:1) Because all Numbers are Words, if any Numbers exist, then some Words are Numbers.2) Existence of Numbers is guaranteed by “some locks are numbers.” Hence Conclusion I is necessary.3) Those Locks that are Numbers are also Letters (Numbers ⊆ Letters). Therefore “Some locks are letters” is necessary (Conclusion II).

Verification / Alternative check:Mark an element that is both Lock and Number; propagate along the universal chain to confirm it is a Letter and therefore a Word.

Why Other Options Are Wrong:Any option omitting I or II ignores either the existential support or the universal chain.

Common Pitfalls:Failing to leverage the guaranteed existence from a “some” premise before applying universal inclusions.

Final Answer:Conclusions I and II follow.