# Test T2

This 55-minute test was designed to let the students experience how to combine mathematical concepts and concrete application together.

Common Mistakes:

• In Part I, some students wrote things like $\forall y x\vee y$ which are not wff in $\mathcal{F}$. Few students came up with $A$ in which there are no free occurrences of $x$. In this case, $t_1$ is always free for $x$ in $A$.
• In Part II and Part III, students really need to recall the exact statements of the definitions of different rules and check whether they are applied correctly.
• In Part IV, many students still have difficulties in deciding the positivity or the negativity of the occurrence of a quantifier in a rectified wff.
• In Part V, some students have redundancy in their answers. For instance, in DNF, components like $[p\wedge\sim p]$ should be abandoned, since they are always false. Also in CNF, components which always take truth value are redundant.
• In Part VI, some students didn’t state the Substitution-Value Theorem correctly for A, but most of them did correctly in B.