Logic Symbols

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Logic Symbols are part of a modern logical system for expressing rational thought and common patterns of reasoning. These symbols are used to clearly represent often times highly complex logical relationships between statements. There are five special symbols that are employed as statement connectives or operators; these are the logical symbols. The five logical symbols are all truth-functional connectives and will be discussed in more detail below. The symbols are ~ (also symbolized as �), & (also symbolized as or ^), v, (also symbolized as ⊃), and <-> (also symbolized as ). Logical symbols are used in a language that has several parts. Propositions are the statements that can be either true or false. These individual statements are usually represented by capital letters of the alphabet and are called statement constants. They are normal declarative sentences but are represented by statement constants for convenience. The statement connectives are the logical symbols whose function is to form new compound statements. These connectives can be reapplied to the resulting compound statements to form new compounds of compounds.
Symbol
Symbol Name
Meaning/Definition
Example
1) ⋅ And And a ⋅ b
2) ^ Caret/Circumflex And a ^ b
3) & Ampersand And p & q
4) + Plus Or o + m
5) ⋁ Reversed caret Or p ⋁ q
6) ∣ Vertical line Or x ∣ y
7) ' Single quote Not negation p'
8) - Bar Not negation p-
9) ¬ Not Not negation ¬ o
10) ! Exclamation mark Not negation !x
11) ⊕ Circled plus/ oplus Exclusive or - xor p ⊕ r
12) ˜ Tilde Negation ˜x
13) ⇒ Implies
14) ⇔ If and only if
15) ∀ For all
16) ∃ There exists
17) ∄ There does not exists
18) ∴ Therefore
19) ∵ Because/ Since


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