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What is a non sequitur?

What is a non sequitur? Here are some definitions.

Noun
  1. Any abrupt and inexplicable transition or occurrence.
  2. Any invalid argument in which the conclusion cannot be logically deduced from the premises; a logical fallacy.
  3. A statement that does not logically follow a statement that came before it.
  4. (humor) A kind of pun that uses a change of word, subject, or meaning to make a joke of the listener’s expectation.
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Examples
Confronted yesterday with the Senate report, Wilson could only offer a non sequitur and a lame denial.
As an argument, though, it has the disadvantage of being a complete non sequitur.
The reason this inference amounts to a logical fallacy is that it is just a blatant non sequitur.
This unusual non sequitur represents the high point of bizarreness in this collection of sketches.
First of all, common sense would dictate that this is a non sequitur, because the federal and state education collusion is a monopoly itself.
This non sequitur is even harder to sustain when considering the Asian minority, a minority that has had its own historical hardships.

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