Question

Help with symbolic logic.
Simplify
~[~(p∧q)→~q]∨q

Where:
~ means negation
∧ means conjuction
∨ means disjuction
→ is the condicional.


Seems easy , but i'm missing some rule

Answer 1

\neg is typically used to denote the logical negation operation on atomic formula

Answer 2

What is your definition of 'simplify'? In what form do you want that expression?

Answer 3

I have this formula: p→q = ~p∨q.
So simplify is find a shortest equivalent expression

Answer 4

Why don't you create a truth table

Answer 5

I did it, and was useless.
The answer is supposed to be "q", but i dont know how to reach that

Answer 6

~P -->~Q implied that Q--> P so, the inner of the first term turns to q-->(p and q)

Answer 7

I need latex for easy step up, please, post some code for imply (-->) and (^) or (v) . then I can copy that code

Answer 8

\ [p \rightarrow q\] (-->)
\[p \rightarrow q\]

\ [p\neg q\]
\[p\neg q\]

I cant find the ^

Answer 9

\[ q\wedge p\]

Answer 10

ok, so in the inner stuff, you have \[q\rightarrow (p\wedge q)\]

Answer 11

consider the (p and q ) as a wholething, you have formula for \[q\rightarrow something= \neg q\vee something\]

Answer 12

that means you have the inner turns to \[\neg q \vee (p \wedge q)\]

Answer 13

before it, you have negative, now open it, you get \[q\wedge \neg (p\wedge q)\] got it?

Answer 14

after them you still have \[\vee q\]so, the whole turns to
\[q\wedge \neg (p\wedge q)\vee q\]

Answer 15

I Got it, thanks.