State/A OR B is logically equivalent to NOT A IMPLIES B

Logical Connections

This statement logically relies on the following definitions and statements: Def/Language of set theory, Def/Free variable, Def/Logically equivalent, Def/Boolean conjunction

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Below are the truth tables for $A \vee B$ and $(\neg A) \Rightarrow B$, computed using the truth tables for the boolean conjunctions OR and IMPLIES, as well as NOT.

Hence $A \vee B$ is logically equivalent to $\neg A \Rightarrow B$.