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Each of these is a little awkward; you have to read them carefully. We applied the first rule to the first part of the statement, which required then negating the inner part, for which we can apply the second rule. Here is a question about the former, from But I suspect that Sarah already knew that. Your email address will not be published.

The pragmatics of descriptive and metalinguistic negation: experimental data from French

This site uses Akismet to reduce spam. Learn how your comment data is processed. Skip to content Last time, I started a series exploring aspects of the translation of English statements to or from formal logical terms and symbols, which will lead to discussions of converse and contrapositive, and eventually of logical arguments. What does negation mean?

What is Negation? (Applied Logic Series)

Doctor Teeple started with the concept of a statement: To negate a statement, you write the opposite of what the statement says. But before we talk about the opposite of a statement, let's talk about the statements themselves. A statement is pretty much what it sounds like it should be.

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It's an equation or sentence or a declaration of some sort. It doesn't matter whether the statement is true or false ; we still consider it to be a statement. For example, I could say, "The sky is purple" or "The earth is flat. I could say, "The U. We can negate each of these statements by writing the opposite of what it says. So for example, the negation of "The sky is purple" is "The sky is not purple.

[Discrete Mathematics] Rules of Inference

We make statements and negate them without judging whether they are true or false. That is another issue.

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But once we are given that a statement is true or false, we can note what happens to the statement when we negate it. For example, suppose we know the following: "The sky is purple.

What is Negation?

Negation turns a true statement into a false statement and a false statement into a true statement. Now, all of the statements we have been working with are sentences. We can also do this with math equations. I want to warn you to be on the watch for statements that contain words like "for every ," "for all ," or "there exists. Here's an entry in the Dr. Math archives that might help: This leads us to the next question, from Negating quantifiers all, some, none Negation in Logic What is the negation of the sentence "In every village, there is a person who knows everybody else in that village.

My guess is "In at least one village, there is at least one person who knows at least one person in that village.

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Doctor Mike saw that Thomas needs to start simpler, so he turned the latter part of the statement temporarily into a single phrase, which can be a very helpful technique: Close, but not quite there. Think of it this way. The negation should be: "In at least one village, each person does not know everyone else. In general, for language exercises like this, there are two basic rules. The negation of a sentence like " For every Or if we rewrite it in terms of the original statement we get "You are not rich and not happy.

Again, let's analyze an example first. Consider the statement "I am both rich and happy. Negation of " If A, then B". This might seem confusing at first, so let's take a look at a simple example to help understand why this is the right thing to do.


Consider the statement "If I am rich, then I am happy. So the negation of " if A, then B" becomes "A and not B". Now let's consider a statement involving some mathematics. Although the phrasing is a bit different, this is a statement of the form "If A, then B. For this statement to be false, all we would need is to find a single integer which is not even and not odd.