# 简答题
<ol>
  <li>What is the definition of validity for a propositional logic formula?</li>
  <li>Please explain how to determine whether a given propositional logic formula with CNF is valid.</li>
  <li>Please illustrate the different treatment for free and bound variables in the semantical evaluation of a predicate logic formula.</li>
  <li>Please state the key idea of program verification using model checking techniques.</li>
</ol>

# 计算题
<ol>
  <li> Convert the following formula into CNF and give its parse tree: $(p \vee q \rightarrow r ) \rightarrow r \vee s$ </li>
  <li> Translate the following statements into predicate logic formula: </li>
  <li> model checking</li>
</ol>

# 证明题
<ol>
  <li> Prove the following statement: $(p \wedge q) \rightarrow r \vdash (p \rightarrow r) \vee (q \rightarrow r)$</li>
  <li> Prove the following sequent doesn't hold using semantical evaluation:
  $\forall x \exists y P(x,y) \models \exists y \forall x P(x,y)$</li>
  <li> Prove the total correctness of the following hoare triplet: $\{ x \geq 0 \wedge y > 0 \} Div \{ y=d*x+r \wedge r < y \}$</li>
  
  ```cpp
    Div:
      {pre-condition}
      r = y;
      d = 0;
      while(r >= y){
        r = r - y;
        d = d + 1;
      }
      {post-condition}
  ```
</ol>