Negation : Not (logic) 

The negation of the statement p is written in various ways:

• ~p;
• ¬p;
• p (which is p with a bar over it);
• NOT p;
• !p

~p is true if and only if p is false. For instance, if p denotes the statement "today is Saturday", then its negation ~p is the statement "today isn't Saturday".

In classical logic, double negation means affirmation; i.e., the statements p and ~(~p) are logically equivalent. In intuitionistic logic, however, ~~p is a weaker statement than p. Nevertheless, ~~~p and ~p are logically equivalent even intuitionistically.

Logical negation can be defined in terms of other logical operations. For example, ~p can be defined as p → F, where → is material implication and F is absolute falsehood. Conversely, one can define F as p & ~p for any proposition p, where & is logical conjunction. The idea here is that any contradiction is false. While these ideas work in both classical and intuitionistic logic, they don't work in Brazilian logic[?], where contradictions are not necessarily false. But in classical logic, we get a further identity: p → q can be defined as ~p ∨ q, where ∨ is logical disjunction.

Algebraically, logical negation corresponds to the complement in a Boolean algebra (for classical logic) or a Heyting algebra[?] (for intuitionistic logic).

could be recast as a limitation. . . . The power to purpose does not allow the government.html">government.html">government.html">government.html">government.html">government to exclude all. (1996) (Kennedy, J., concurring in the judgment). imposes some limits on the state's ability to adopt.html">adopt content-based what those limits are is unclear, and presents a difficult "cases have not yet determined . . . that government's decision necessarily subject.html">subject to the highest level of scrutiny. Must a if it builds a band shell in the park and dedicates it solely to Denver, 518 U.S. at 750 (plurality opinion); see also (1975) (Rehnquist, J., dissenting) ("May an opera house limit its municipal theater devote an entire season to Shakespeare, or is served basis?"). Supreme Court's jurisprudence on this question. In particular.html">particular, range of speech that the government chooses to subsidize (whether indirectly, through the creation of a public forum) the more content-based distinctions. particular message that the government seeks to disseminate. In government chooses to subsidize are clearly subject to at most permissible. For example, "[w]hen Congress established a adopt democratic principles, 22 U.S.C. Sec. 4411(b), it was not competing lines of political philosophy such as communism and Velazquez, 531 U.S. at 541 ("[V]iewpoint-based funding decisions the speaker, or in instances, like Rust, in which the government own program.") (internal quotation marks and citation omitted). unconstitutional conditions cases, such as Rust and Velazquez, restrictions on the use of public fora. This is because the .

 On wordlookup.net  

All is still licensed under the GNU FDL.
It uses material from the wikipedia.