Final answer:
The given conclusion doesn't logically follow from the syllogistic premises, but the terms can still be identified. The major term is 'programmers', the minor term is 'mathematicians', and the middle term, had it been logically connected, would likely be 'computer scientists'.
Step-by-step explanation:
Your reasoning is attempting to draw a conclusion using syllogistic logic, which is the basis for deductive reasoning in logic and mathematics. However, it looks like there might be a logical fallacy as the conclusion doesn't necessarily follow from the premises. But first, let's address the components of the syllogism concerning your options:
For conclusion
-Major term is the predicate; Minor term is the subject; Middle term appears in both premises but not in the conclusion.
In the statement 'All programmers are IT; Some computer scientists are mathematicians; Therefore, some mathematicians are programmers.', the actual conclusion does not logically follow from the premises. However, if we apply the structure to identify major, minor, and middle terms, we get:
-The major term is 'programmers' because it is the predicate in the conclusion.
-The minor term is 'mathematicians' because it is the subject in the conclusion.
-The middle term should be the term that connects the two premises, which in this case could have been 'computer scientists' had the conclusion followed logically.
With these definitions, the most accurate option from your list is b) The middle term is computer science and the minor term is mathematical, although it would be more precise to say that the minor term is 'mathematicians' rather than 'mathematical'.