Mister Exam

Mathematical logic signs and operations

Here is the table of signs and operations, which using in mathematical logic, also denote What are priorities of using operations if there aren't brackets in the logic expression.

¬a
    - negative
a⇒b
    - implication
a∧b
    - conjunction
a∨b
    - disjunction
a⇔b
    - logical equality
a⊕b
    - Exclusive or
a|b
    - Nand (Sheffer stroke)
a↓b
    - Nor (Pierce-Arrow)

Table with priorities:

+----------+---------------------------------+--------+
| Priority | Operation                       | Symbol |
+----------+--------------------------+------+--------+
| 7        | Not                      | NOT  | ¬      |
+----------+--------------------------+------+--------+
| 6        | And                      | AND  | ∧      |
+----------+--------------------------+------+--------+
| 5        | Or                       | OR   | ∨      |
+----------+--------------------------+------+--------+
| 5        | Exclusive or             | XOR  | ⊕      |
+----------+--------------------------+------+--------+
| 4        | Not-And (Sheffer stroke) | NAND | |      |
+----------+--------------------------+------+--------+
| 3        | Not-Or (Pierce-Arrow)    | NOR  | ↓      |
+----------+--------------------------+------+--------+
| 2        | If, then                 | IMP  | ⇒      |
+----------+--------------------------+------+--------+
| 1        | Equivalent to            | EQU  | ⇔      |
+----------+--------------------------+------+--------+

Or as the picture:

Mathematical logic signs and operations

The mathematical logic calculator itself can determine the priority of operations automatically:

If you entered:

0↓1|a↓a^bvd=>x↓c|1↓0

  • converted to

    0↓(1|a)↓((d∨(a∧b))⇒x)↓(c|1)↓0

    The calculator will also simplify this boolean expression:

    a∧c∧(¬x)∧(b∨d)