Question on DeMorgan’s Law Theory

hihihi9993

According to DeMorgan's Law Theory, And becomes Or when contrapositive. Correct?

Then, I wonder why
A if and only if A (AB = A->B AND B->A)
becomes /A/B (/B->/A AND /A->/B)
instead of /B->/A OR /A->/B

I know that we need AND to satisfy the valid argument, but how do we automatically know that the statement only deals with inclusive or?

Can someone clarify plz? Thanks!

Freddy_D

"If and only if" is a biconditional statement

A<---->B (all As are Bs and all Bs are As)

contraposing this statement would be

B<---->A (All "not Bs" are "not As" andAll "not As" are "not Bs")

DeMorgan's law is not used in the above; instead, it is utilized when you have an "and" or "or" in the sufficient or necessary condition.

Ex. A or B ---> C

becomes

C ---> A andB

hihihi9993

@Freddy_D You are awesome!!!!! Thank you!

Freddy_D

@d931n027h said:
@Freddy_D You are awesome!!!!! Thank you!

You're welcome. Good luck with your studies!