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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: Some giraffes are rhinos. All rhinos are tigers. Conclusions: (I) Some tigers are giraffes. (II) All tigers are rhinos.
Only conclusion (II) follows
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Convert statements to standard categorical propositions (Some A are B, All B are C) and apply standard syllogism conversion and combination rules.
Convert statements to standard categorical propositions (Some A are B, All B are C) and apply standard syllogism conversion and combination rules.
Analyze Statement 1
Some giraffes are rhinos (I-type proposition). This means there is an intersection between the set of Giraffes and Rhinos.
Analyze Statement 2
All rhinos are tigers (A-type proposition). This means the entire set of Rhinos is contained within the set of Tigers.
Evaluate Conclusion I
Some giraffes are rhinos + All rhinos are tigers gives 'Some giraffes are tigers', which converts directly by simple conversion to 'Some tigers are giraffes'. Conclusion I follows.
Evaluate Conclusion II
All tigers are rhinos is the reverse (conversion) of 'All rhinos are tigers', which only holds as 'Some tigers are rhinos'. Thus, Conclusion II does not follow.
A: Only conclusion (II) follows is incorrect because conclusion II is false. B: Neither conclusion follows is incorrect because conclusion I is true. D: Both conclusions follow is incorrect because conclusion II is false.
C is correct because only conclusion (I) logically follows from the given statements through standard syllogism rules.
In affirmative categorical syllogisms ('Some' and 'All'), a universal statement ('All A are B') does not convert to 'All B are A' without a restriction; it only converts to 'Some B are A'.
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