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In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a man is a necessary condition for being a brother, but it is not sufficient—while being a man sibling is a necessary and sufficient condition for being a brother.
3. P is not necessary but it is sufficient: If (P OR Q) then S. We don't NEED P. We can get S from Q. But on the other hand if we DO have P, P is enough in itself to create S. No need for anything else. 4. P is not necessary AND not sufficient: If (P OR Q) AND R then S. P is not necessary. We can get S from Q even though we do not have P.
Many office suites, such as Microsoft Office and LibreOffice, are equipped with spelling and grammar checkers that are on by default.Open the Wikipedia article, select "edit" from the menu atop the page or section, select and copy the article source, paste it into a Word or Writer document, follow the red (spelling) and green (grammar) markers, and correct mistakes as necessary.
Let be a regular language. Then there exists an integer depending only on such that every string in of length at least (is called the "pumping length") [4] can be written as = (i.e., can be divided into three substrings), satisfying the following conditions:
Necessary But Not Sufficient is a 2000 novel authored by Eliyahu Goldratt with co-authors Eli Schrangenheim and Carol A. Ptak. Necessary But Not Sufficient is written as a "business novel" and shows the fictional application of the theory of constraints to enterprise resource planning (ERP) and operations software and organizations using that software.
Don't worry about relying on your browser's spell check feature. With AOL Mail, click one button to check the entire contents of your email to ensure that everything is spelled correctly. In addition, you'll never need worry about typos or misspelled words again by enabling auto spell check.
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