Question on DeMorgan’s Law Theory

hihihi9993hihihi9993 Member
in General 347 karma

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! :)

Comments

  • Freddy_DFreddy_D Core Member ⭐
    2989 karma

    "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

  • hihihi9993hihihi9993 Member
    347 karma

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

  • Freddy_DFreddy_D Core Member ⭐
    2989 karma

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

    You're welcome. Good luck with your studies!

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