For example, if A is valid, but B is not valid, the respective truth-values
would be “A = 1” and “B = 0.”
If proposition “A OR B” is applied, this equates to “1 OR 0,” indicating
that the proposition is logically true. However, if proposition “A AND B”
is applied, this becomes “1 AND 0,” which would be logically false.
The combination of these truth-values is referred to as a “truth table.”
Logical product
(AND)
Negation
(NOT)
B
AORB
A
B
AANDB
A
NOT A
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
Logical Operations
A “logical operation” is a type of mathematical operation that is used when a
combination featuring multiple conditions (logic) is represented by an expression.
Basic theory
Truth table
A
Reference
Chapter 7
Logical sum
(OR)
7-1-2 Applied mathematics
The analysis of accumulated data allows for the discovery of operational
problems and may provide hints that lead to the improvement of operational capabilities. During this process, “applied mathematics” is used.
Applied mathematics is a branch of mathematics concerned with areas
such as “probability” and “statistics,” which aims to impart mathematical understanding to non-mathematical fields.
1
Probability
“Probability” is a means to evaluate the total number and extent of accumulated data.
(1)permutation
A “permutation” is the aggregate derived when an optional count is taken
from a particular collection of data, and the remaining values are arranged
in an equation.
If r is arbitrarily taken from the variant n, and a sequence of the resulting
numbers arranged in one row is expressed as nPr, the following expression
is provided.
Pr = n × (n − 1) × (n − 2) × ··· × (n − r + 1)
n
Example
Take four variant numbers from the values “1, 2, 3, 4, 5, 6” to derive four separate digits.
P =6×(6−1)×(6−2)×(6−3)=6×5×4×3=360
6 4
162