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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
In a stunning non sequitur, he then proposes a set of reforms aimed at raising the absolute position of unskilled workers, such as a higher minimum wage.
Second, linking logging of mature trees to clearing of underbrush is a policy non sequitur.
This non sequitur is even harder to sustain when considering the Asian minority, a minority that has had its own historical hardships.
The reason this inference amounts to a logical fallacy is that it is just a blatant non sequitur.
First of all, common sense would dictate that this is a non sequitur, because the federal and state education collusion is a monopoly itself.
She gave him a slightly scornful glance, and he racked his brains to see if he could find the reason for the non sequitur.

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