Question

Is the reason \[(A \implies B \equiv (\sim A) \wedge B)\] because the implication is true if 1) premise is false (~A) or if 2 conclusion is true (B)?

Answer 1

\[A \implies B\]
is equivalent to
\[\hbox{~} \ (A \wedge \hbox{~} \ B)\]

Just draw up the truth table and compare the values of these tho statements for
A true, B true
A true, B false
A false, B true
A false, B true

and you'll find they are exactly coincident.

Answer 2

...these TWO statements for ...