A commuted sentence?

Sandy, Utah

The book review continues

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy) 

Key symbols

≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore . = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable = Conjunction meaning And 0
 = Null class
cls = Class
int = Interpretation

Langer, page 211. Symbolic logic has rules within which much be applied and understood by the presenter, in order for equations and arguments to make sense to the reader. There are rules of manipulation in place.

Langer, page 212. The author is establishing a law within symbolic logic by which a + b or b + a can as a sum be commuted, as in making the same result whether added or multiplied. Therefore, (a + b) or (b + a) can be expressed as (b x a) or (a x b).

Langer, page 212. Here addition and multiplication are being expressed through commutation, as equal, therefore, (a x b) + (a x c) is equated as (a x (b + c).

As confusing as this work from Langer can appear for me without prayerful consideration and serious concentration, I actually can make sense of this as I am learning.

Using

(a x b) + (a x c)

and then

(a x (b + c)

Consider

(3 x 3) + (3 x 3) equals 18

(3 x (3 + 3) equals 18

In earlier reviews, a, b, c were all equated.