There is a close relationship between material equivalence and logical equivalence.
2.
Logical equivalence is different from material equivalence.
3.
The exclusive or is also equivalent to the negation of a logical biconditional, by the rules of material implication ( a material conditional is equivalent to the disjunction of the negation of its material equivalence.
4.
In the first chapter, Frege defines basic ideas and notation, like proposition ( " judgement " ), the universal quantifier ( " the generality " ), the conditional, negation and the " sign for identity of content " \ equiv ( which he used to indicate both material equivalence and identity proper ); in the second chapter he declares nine formalized propositions as axioms.
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