Discrete Mathematics | Propositional Logic | Test 1 | Question: 7

Question

The $\textit{well-formed formulas (wff)}$ of propositional logic are obtained by using the following rules:

 1. An atomic proposition $\phi$ is a well-formed formula.
 
 2. If $\phi$ is a well-formed formula, then so is $\neg \phi.$
 
 3. If $\phi$ and $\psi$ are well-formed formulas, then so are $(\phi \vee \psi), (\phi \wedge \psi), (\phi \rightarrow \psi),$ and $(\phi \leftrightarrow \psi).$          
         
 4. If $\phi$ is a well-formed formula, then so is $(\phi).$  

Now, consider the following statements:   
    
$1.\neg (\neg P \wedge \neg \neg R)$
   
$2.\neg(P,Q,\wedge R)$   
    
$3.(\neg P)(\neg Q)\wedge (\neg P)$

$4.(P\vee Q)(P\vee R)$   
   
$5. (P) \vee (\neg P)$   
   
$6. P \rightarrow (\neg Q)$   
   
$7. (\neg \neg \neg \neg P)$  
     
(P, Q and R are atomic propositions)   

Total number of well-formed formulas are ______

Comments

@[Student] it is author dependent. I could show some good resource where parentheses are not mentioned for rule 3. Rules should be mentioned in the question.

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@ankitgupta.1729 If possible share the resource. Thanks for the quick clarification appreciable.

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