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:


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

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Pepsi, only danker

"Bepis is my favorite carbonated beverage"

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

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

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This symbol represents the boolean value "false".

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Flakko •¥• Shack Co

The unbrakable courage of percistence

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Is defined as

Specifies the definition of something.

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Join \ Bowtie

The Join/bowtie is commonly used in logic math and seen as philosophically symbolic.

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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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Math operation first number added to summation of itself times base counted down for each digit place until the ones column 10^0.

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negation (not)

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

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

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Means a statement is provable

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set equal to

Define the value of a variable as equal to constant or to value of another variable.

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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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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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