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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: No door is a lock. No lock is a key. Conclusions: I. No door is a key. II. No lock is a door.
Both conclusions I and II follow
Only conclusion II follows
Only conclusion I follows
Neither conclusion I nor II follows
Only conclusion II follows
Apply the rule: No A is B and No B is C means no direct relationship is established between A and C, therefore, negative conclusions connecting A and C are inconclusive.
Apply the rule: No A is B and No B is C means no direct relationship is established between A and C, therefore, negative conclusions connecting A and C are inconclusive.
Analyze the statements
Statement 1: No door is a lock. Statement 2: No lock is a key. This defines a relationship where 'Door' and 'Key' are both disconnected from 'Lock', but they may or may not overlap with each other.
Evaluate Conclusion I
Conclusion I: 'No door is a key'. Since there is no explicit information linking Doors and Keys, we cannot conclude that no door is a key. This conclusion does not necessarily follow.
Evaluate Conclusion II
Conclusion II: 'No lock is a door'. The statement 'No door is a lock' is logically equivalent to 'No lock is a door' through the process of conversion in categorical syllogism. Thus, Conclusion II follows.
A: Both conclusions do not follow because I is not definitively true. C: Only I does not follow as it is not supported by the statements. D: Neither follows is incorrect because II is a valid conversion of the first statement.
B is correct because the statement 'No door is a lock' is equivalent to 'No lock is a door' (Conclusion II), while the relationship between 'door' and 'key' remains undetermined (making Conclusion I invalid).
Remember that 'No A is B' converts to 'No B is A'. Always check for direct links in syllogisms; if no bridge exists between two subjects, any definite relationship claimed between them is False.
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