LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
Some key symbols from the textbook:
≡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
Joint Inclusion or Disjunction of Classes
Two classes may be related to a third class. Taking the two classes, class A and class B, together in one class, this class contains everything that belongs to class A or class B, therefore, it is called the sum of class A and class B. (139). This would be expressed like a mathematical term, as A + B. (140).
Langer introduces the symbolic symbol V, a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives). (140).
Symbolic logic
Cited
'The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false.'
The author writes the example:
'(x ε A) V (x ε B)' (140).
X is A is true as is X is B
Based on Langer's example
(x) : (x ε A) V (x ε B) ⊃ (x ε A + B)
X equals X is A is true as is X is B is the same as X is A plus B
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