Give 5 examples of invalid Syllogism and Justify its invalidity.

1:   All Snakes are reptiles   

      Therefore, some reptiles are crocodiles

If an argument has less than three terms (i.e. two terms), we cannot call it a syllogism, rather it is a case of immediate inference. It violates rule number one.

2.  All dogs are a quadruped.

     All cats are a quadruped.

     So, all cats are dogs.

In both the premises, the middle term is undistributed (since A proposition doesn't distribute its predicate). No conclusion is possible as the middle term is not properly connected with the extremes. When this rule is violated we commit the fallacy of undistributed middle.  It violates rule number three.

3. All men are rational.

    All men are a biped.

    Therefore, all bipeds are rational.

Here the minor term 'biped' (subject term of conclusion) is distributed which is not distributed in the minor premise (being the predicate of A proposition). So the fallacy committed in this argument is illicit minor. It violates rule number four.

4. No artists are rich persons.

    Some rich persons are not theists.

    Therefore, some theists are not artists.

Since both the premises are negative, the conclusion (some theists are not artists) is not valid and we commit the fallacy of two negative premises or fallacy of exclusive premises. It violates rule number five.

5. No poets are scientists.

    Some philosophers are poets.

   Therefore, some philosophers are not scientists.

This conclusion (negative one) is a valid conclusion. But if we draw any affirmative conclusion (such as "Some philosophers are scientists") from the above premises, it would be a fallacious conclusion. Here, we would have committed the fallacy of drawing an affirmative conclusion from a negative premise. Similarly, we can prove that if the conclusion is negative, one of the premises must be negative It violates rule number six.