Embedded Conditional vs DeMorgan's

mt10087

Is there a difference between A --> (B-->C) vs A --> B or C

If so, what is the contrapositive of the A --> (B-->C)

akistotle

It’s different. A --> (B-->C) = A and B —> C

Contrapositive: /C --> /A or /B

Rigid Designator

Yes there is a difference since B --> C and B or C have different truth tables.

To get the contrapositive of A --> (B --> C) you negate the consequent, which is (B --> C) in this case, then flip the conditional and negate the antecedent, which is A.

So you get /(B --> C) --> /A.

The only truth value assignment which would give you a negation of B --> C is where B is true but C is false. So basically /(B --> C) --> /A amounts to saying if B is T and C is F then /A.