Rule 5: If either premise in a syllogism is negative, the conclusion must also be negative.
 
This Rule is simply a logical extension of Rule 4, supra. If ANY syllogism has one negative premise (a result that is clearly permitted by Rule 4, supra), then its conclusion MUST also be negative. Consider the following example:
 
1. NO man is immortal. (major premise)

2. Socrates is a man. (minor premise)

3. Socrates is NOT immortal. (conclusion)
 
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Because one of the premises in this syllogism is negative (i.e., in this case, the major premise), the conclusion must also be negative. The same would be true if only the minor premises had been negative as well.