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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! :)
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3 comments
@donamhyun690 said:
@6400 You are awesome!!!!! Thank you!
You're welcome. Good luck with your studies!
@6400 You are awesome!!!!! Thank you!
"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