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Anyone who says that any one of these syllogisms is invalid because one of the terms is “God,” does not have any idea what the science of Logic is about.

Well when you omit VERY important data as in Mary, Sam, and Dorothy were all created beings and created by The Word of God, that makes your approach...incomplete.

I will point out that the Apostles when penning the Gospels and Acts do not engage in your gymnastics. They say "Mary the mother of Jesus."

But you are free to infer all you want. But that can become a dangerous exercise when dealing with the revealed written Word of God:

Compare the following:

God:

“Of every tree of the garden you may freely eat; 17 but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.”

Someone else:

4 Then the serpent said to the woman, “You will not surely die. 5 For God knows that in the day you eat of it your eyes will be opened, and you will be like God, knowing good and evil.”