But there is a difference between || and |. The former: As long as A is true, the value of B is not calculated. The latter is not. It calculates the value of the formula before and after | before continuing. ...
In logic, a set of symbols is often used to represent the logical structure. Because logicians are very familiar with these symbols, they don't explain them when they are used. Therefore, the following table lists the symbols commonly used by logic learners and their names, pronunciations and related fields of mathematics. In addition, the third column contains informal definitions and the fourth column gives short examples.
It should be noted that in some cases, different symbols have the same meaning, while the same symbol has different meanings according to the context.
Basic logical symbol
Example of symbolic name interpretation
Read aloud or read aloud or read aloud ancient poems.
kind
→
Substantive meaning a? B means that if A is true, then B is also true; If a is false, it has no effect on B.
→ Maybe it means the same thing? The same meaning (this symbol can also be the domain and adjoint domain of the index function; See table of mathematical symbols).
Maybe it means the same thing? The same meaning (this symbol can also mean superset). x = 2？ X2 = 4 is true, but x2 = 4? X = 2 is generally false (because x can be? 2)。
Implication; If .. then
propositional logic
Substantial equivalence a? B means that if B is true, A is true, and if B is false, A is false. x + 5 = y +2？ x + 3 = y
If and only if; Under the condition of … and only under the condition of …
propositional logic
Logical negative statement? If and only if a is false, a is true.
Slash and "?"that cross other operators. The same is put in front of it. . ? (? a)？ A
x ≠ y？ ? (x = y)
Say "no"
propositional logic
∧ Logical conjunction statement A ∧ B is true, if both A and B are true; Otherwise it's fake. n & lt4∧n & gt； 2 ? When n is a natural number, N = 3.
and
propositional logic
∨ Logical disjunction statement A ∨ B is true, if A or B (or both) is true; If both are false, the statement is false. n ≥ 4 ∨ n ≤ 2？ N ≠ 3 When n is a natural number.
or
propositional logic
⊕
XOR declares that A ⊕ B is true, and it is true when A or B is true, but not at the same time. Answer? It means the same thing. (? A) A is always true and A is always false.
XOR operation
Propositional logic, Boolean algebra
Full name quantifier? X: P(x) means that all x makes P(x) true. ? n ∈ N: n2 ≥ n。
For all; For any; For each
predicate logic
Existential quantifier? X: P(x) means that at least one x makes P(x) true. ? N ∈ N: n is even.
have
predicate logic
! Unique quantifier? ! X: P(x) means that there is an exact x that makes P(x) true. ? ! n ∈ N: n + 5 = 2n。
There is one.
predicate logic
:=
≡
:? Defining x := y or x ≡ y means that x is defined as another name for y (but note that ≡ can also mean other things, such as congruence).
p:？ Q means that p is defined as logically equivalent to q. cosh x := (1/2)(exp x+exp (? x))
A XOR B:？ (A ∨ B) ∧？ (A ∧ B)
be defined as
All places
() Priority combination gives priority to the operation in parentheses. (8/4)/2 = 2/2 = 1，8/(4/2) = 8/2 = 4。
All places
Inference x y means that y is derived from x A → B ├? B →? A
Inference or deduction