Proving the negation of conditional via propositional calculus

Question

Prop. Calc

https://www.dropbox.com/s/2dpk7fvae668phn/Screenshot%202016-03-03%2018.13.42.png?dl=0

Hi, I'm trying to prove the negation of a conditional.
Basically, prove ¬(α → b) is equivalent to α ∧ ¬b.
I've figured out to prove ¬b, but I can't seem to get a using the rules of inference.

Any hints would be appreciated.

score 0 · Answer 1 · answered Mar 03 '16 at 23:31

0

$$\begin{align*} \neg (a \to b) &\equiv \neg ( \neg a \vee b) \\ &\equiv \neg(\neg a) \wedge \neg b \\ &\equiv a \wedge \neg b \end{align*}$$

answered Mar 03 '16 at 23:31

Stefan Mesken

16,651

I know (a→b)≡(¬a∨b) is a definition, but I don't know if I can use it in the above software. – user1869558 Mar 03 '16 at 23:38
@user1869558 I know nothing about that piece of software... Sorry. – Stefan Mesken Mar 03 '16 at 23:46

Proving the negation of conditional via propositional calculus

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