5 operations and 9 algebra laws of logic

Содержание и основные понятия

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Alterna · Chapter 17 · page 17.1
5 operations and 9 algebra laws of logic
Table of laws + interactive formula simplifier.
Boolean algebra
It is a set of laws to simplify the logical expression. Knowledge of the nine key laws saves hours on the EGE No. 2 and No. 15. Most of the tasks are to apply the de Morgan law or to absorb it.
GEF
PIF
OGE No. 2.4
EEG No. 2.15
01
9 laws of algebra logic
№
Law
For ♪
For ♪
1
Impotence
A∧A = A
A∨A = A
2
Commutability
A∧B = B∧A
A∨B = B∨A
3
Association
(A∧B)∧C = A∧(B∧C)
(A∨B)∨C = A∨(B∨C)
4
Distributiveness
A∧(B∨C) = (A∧B)∨(A∧C)
A∨(B∧C) = (A∨B)∧(A∨C)
5
Absorption
A∧(A∨B) = A
A∨(A∧B) = A
6
Sticking
(A∧B)∨(A∧¬B) = A
(A∨B)∧(A∨¬B) = A
7
Supplement
A∧¬A = 0
A∨¬A = 1
8
Zero element
A∧0 = 0
A∨1 = 1
9
De Morgan.
¬(A∨B) = ¬A∧¬B
¬(A∧B) = ¬A∨¬B
The law of binding
Of particular importance in the EGE No. 2:
(A∧B)∨(A∧¬B) = A
This "clicks" two similar situations that differ only by one variable.
02
Examples of simplification
Example 1: (A)B(A)b)
(A∧B)∨(A∧¬B) = A∧(B∨¬B) = A∧1 =
A
Example 2: B(A)B(A~C)
¬(A∨B) = ¬A∧¬B (де Морган)
(¬A∧¬B)∧(A∨C) = (¬A∧¬B∧A)∨(¬A∧¬B∧C) = 0∨(¬A∧¬B∧C) =
¬A∧¬B∧C
Example 3: A (BA)(B)
A∨(¬A∧B) = (A∨¬A)∧(A∨B) = 1∧(A∨B) =
A∨B
03
Simplifying formulas
Enter the formula - see the truth table and the simplified view
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Simplifier of expressions
Formula
04
Mini test
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7 issues by law