Statements: I – Some S are L II – Some C are P III – All P is R Conclusions:…

Concept:

In categorical syllogisms, a conclusion between two terms is valid only when the statements connect them through a shared middle term. When a particular-affirmative premise (‘Some X are Y’) combines with a universal-affirmative premise on the same term Y (‘All Y are Z’), the overlap between X and Y is carried entirely into Z, so ‘Some X are Z’ follows as a necessary consequence. Conversely, if two conclusion terms are never linked by any premise (directly or through a chain of shared terms), no conclusion connecting them can be validly drawn — regardless of what other statements say.

Application:

1. Statement II (‘Some C are P’) establishes that C and P share at least one member.

2. Statement III (‘All P is R’) places every member of P inside R.

3. Since the C–P overlap consists of members of P, and every member of P lies in R, that same overlap must also lie in R.

4. This makes ‘Some C are R’ — Conclusion II — a necessary consequence of Statements II and III.

5. Conclusion I (‘Some P are L’) needs a link between P and L. Statement I relates only S and L; Statements II and III relate P only to C and R. No statement connects P to L, directly or through a shared term.

6. So Conclusion I cannot be validated from the given statements — only Conclusion II follows.

Cross-check:

A quick Venn check confirms this: drawing the C–P overlap inside the R circle (as Statement III requires) automatically forces the C circle to intersect R, verifying Conclusion II. For Conclusion I, the P and L circles can be drawn with zero overlap without contradicting any of the three statements, showing Conclusion I is not forced to be true.

Answer:

Only conclusion II is true.