Conditional reasoning

[VishwaksenaM817]

How do we negate a conditional statement ? Is it even possible ?

[ohthatpatrick]

Yeah, negating a conditional just means
"It's possible that the left side is true and the right side is false"

You don't get a conditional, when you negate a conditional.
You get the existence of at least one counterexample.

We could take an if/then, such as
"If you're a girl, then you like fashion"
and equivalently express it as
"All girls like fashion".

Would you know how to negate the claim "all girls like fashion"?

Sure, it would become "NOT all girls like fashion", which means "at least one girl does not like fashion".

Given the rule
GIRL --> LIKE FASHION

the existence of at least one counterexample looks like
"it is possible that the left side is true but the right side is false" = "it is possible that a girl does not like fashion"

[KayM793]

Sorry...I'm still a bit confused about the steps to negate a conditional. Suppose A--> B. To negate it, we get A--> -B, which is B--> -A. But if we take the contrapositive of the original conditional first, the original conditional becomes -B --> -A. To negate it, the conditional becomes -B --> A, which is -A --> B, the illegal reversal of B--> -A. What did I do wrong??? If I want to take the contrapositive of the conditional, should I negate it first or take the contrapositive first?? Thanks a bunch!!!