Logic Symbols

This page lists of the various symbols in the Logic Symbols group.

In logic, a set of symbols is commonly used to express logical representation. As logicians are familiar with these symbols, they are not explained each time they are used. So, for students of logic, the following table lists many common symbols together with their name, pronunciation and related field of mathematics. Additionally, the third column contains an informal definition, and the fourth column gives a short example.

Be aware that, outside of logic, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings.

Symbols in this group:

and

The statement A & B is true if both A is true and B is true. Otherwise the statement is false.

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Entails

A |= B if for every A that is true, B is true.

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Equivalence

Equivalence is being equivalent or interchangeable. The relationship indicates that both sides are either both true or both false.

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False

This symbol represents the boolean value "false".

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Is defined as

Specifies the definition of something.

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Logical Implication (Implies)

The statement on the left side of the symbol implies the statement on the right side. Can also be read as If, Then, i.e., if "statement on left side", then "statement on right side".

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negation (not)

Negates a logical value, i.e., ! true = false and ! false = true.

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or

The statement "A or B" is true if A or B is true

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Provable

Means a statement is provable

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There exists

There is at least one value of x for which f(x) is true.

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There exists exactly one

There is exactly one value of x for which x is true.

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True

This symbol represents the boolean value "true".

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Universal Quantification

This represents "for all" (or better "for each") or "given any".

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Vertical Bar

The vertical bar (|) is a character with various uses in mathematics, computing, and typography. It may be called by various other names including the polon, pipe (by the Unix community, referring to the I/O pipeline construct), Sheffer stroke (by computer or mathematical logicians), verti-bar, vbar, stick, vertical line, straight vertical line, vertical slash, or bar, glidus, think colon, poley, or divider line.

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xor (exclusive or)

The result of A xor B is true if A is True or B is True but not both True.

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Citation

Use the citation below to add this symbols group page to your bibliography:

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"Logic Symbols." Symbols.com. STANDS4 LLC, 2014. Web. 23 Jul 2014. <http://www.symbols.com/group/85>.

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