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By application of the general syllogistic rules, we will see that there are only 19 valid moods. For the determination of valid mood, we must keep in mind the four figures discussed earlier and important general syllogistic rules discussed. In each figure, there are following sixteen combinations:

A A |
E A |
I A |
0 A |

A E |
E E |
IE |
0 E |

A I |
E I |
II |
0 I |

A 0 |
E 0 |
10 |
0 0 |

Out of these sixteen possible combinations, by application of general syllogistic Rule 5 (i.e. No conclusion follows from two negative premises) we find E E, E O, O E and 0 0 combinations can not yield any valid conclusion.

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Similarly, by applying general syllogistic Rule 8 (No conclusion follows from two particular propositions), combinations like II,I0 and I0 can not yield any valid conclusion. By application of General syllogistic Rule I0, (From particular major and negative minor no conclusion follows) combination IE would not give any valid conclusion.

Thus out of sixteen possible combinations only eight remaining combinations A A, A E, A I, A O, E A, E I, IA and O A are left. Let us examine these remaining combinations to find out which of these combinations can give rise to valid conclusion in which figure.