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What is the negation (logically speaking) of the following proposition:

Today I will do this task.

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    $\begingroup$ Today I will not do this task. $\endgroup$ – David P Sep 28 '14 at 12:00
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    $\begingroup$ $\neg(Today I will do this task.)$ $\endgroup$ – David H Sep 28 '14 at 12:00
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    $\begingroup$ It is not true that I will do this task today. $\endgroup$ – Arnie Bebita-Dris Sep 28 '14 at 12:11
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The negation can be as simple as:

"It is not the case that today I will do this task."

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  • $\begingroup$ this is not what I mean. I mean, should the negation be something like "I will do this task not today or I will do another task today"? $\endgroup$ – mathlearner Sep 28 '14 at 12:26
  • $\begingroup$ All you know is that you will not do the task today. The negation of the statement does not imply that you will do another task today, nor that you will do the task on another day. $\endgroup$ – amWhy Sep 28 '14 at 12:31
  • $\begingroup$ I see. So "I'll do this task tomorrow", "I will not do this task until tomorrow", "I will do this task in 3 or 4 days", "Today I'll complete another task", "Today I'll do another task and tomorrow this one" should all be considered negations (logically)? $\endgroup$ – mathlearner Sep 28 '14 at 12:38
  • $\begingroup$ The negation: "I will not do this task today" encompasses all those possibilities, including "I will never do this task." $\endgroup$ – amWhy Sep 28 '14 at 12:52
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    $\begingroup$ @mathlearner Then you'll be quite busy. There's infinitely many of them. "I'll will not do this task with green eggs and ham", etc $\endgroup$ – David P Sep 28 '14 at 15:00
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You simply try to make the opposite of the proposition "Today I will do this task", such as: "Today is not the case that I will do this task", or "Today I will not do this task".

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