A hypothetical syllogism links conditionals in a chain, using the fact that if P leads to Q and Q leads to R, then P must lead to R. This is a transitive property of the conditional relation and is a recognised valid inference form. It essentially passes the implication through the intermediate step Q.
Option A:
Option A clearly shows the chain P β Q and Q β R leading to P β R, which is valid in standard propositional logic.
Option B:
Option B does not guarantee any relation between P and R; both lead to Q, but nothing links P to R or vice versa.
Option C:
Option C reverses the conclusion and improperly suggests that R implies P, which does not follow from the premises.
Option D:
Option D asserts Q β R, but from P β Q and P β R we cannot generally infer that Q implies R, because Q could arise from other causes without R.
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