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.

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