Question
Three statements are given followed by three
conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All oranges are apples. All apples are grapes. Some grapes are pears. Conclusions: I. Some oranges are pears. II. Some grapes are apples. III. Some apples are oranges.Solution
All oranges are apples (A) + All apples are grapes (A) → All oranges are grapes (A) + Some grapes are pears (I) → No conclusion. Hence conclusion I does not follow. All apples are grapes (A) → Conversion → Some grapes are apples (I). Hence conclusion II follows. All oranges are apples (A) → Conversion → Some apples are oranges (I). Hence conclusion III follows.
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