CMSC 250 Quiz #1 KEY Monday, Sept. 10, 2001

This quiz is to be graded and handed back to the students on Wednesday, Sept. 12, 2001.
  1. [10 pnts.]Determine if each of the following pair of statements is logically equivalent by using a truth table. Use 1 for ``true'' and 0 for ``false'' to complete the truth table.
    1. $(p \wedge q) \vee r$
    2. $ (p \vee r) \wedge (q \vee r)$

    p q r $p \wedge q$ $(p \wedge q) \vee r$ $p \vee r$ $q \vee r$ $ (p \vee r) \wedge (q \vee r)$
    1 1 1 1 1 1 1 1
    1 1 0 1 1 1 1 1
    1 0 1 0 1 1 1 1
    1 0 0 0 0 1 0 0
    0 1 1 0 1 1 1 1
    0 1 0 0 0 0 1 0
    0 0 1 0 1 1 1 1
    0 0 0 0 0 0 0 0

    YES(Yes or No) These statements are logically equivalent.

  2. -2 for the yes/no answer (all or nothing)
    1. [10 pnts.]Give one possible value for the $n$ expressed in each of the following which would make the statement true. (If there is no possible value, write the word ``impossible''.)
      • p = $(n \geq 1)$
      • q = $(n = 3)$
      • r = $(n \leq 7)$
      1. $\sim (p \vee \sim q)$ impossible
      2. $(p \wedge r) \wedge q$ 3

    2. [10 pnts.]Write the contrapositive, converse and inverse of the following logical expression. Do not simplify the expression at all - just give the statement requested in the form you would get from the definition.

      \begin{displaymath} (p \wedge q) \rightarrow (r \vee p) \end{displaymath}

      contrapositive $\sim (r \vee p) \rightarrow \sim (p \wedge q)$
        if simplified : $(\sim r \wedge \sim p) \rightarrow (\sim p \vee \sim q)$
      converse $(r \vee p) \rightarrow (p \wedge q)$
      inverse $\sim (p \wedge q) \rightarrow \sim (r \vee p)$
        if simplified : $(\sim p \vee \sim q) \rightarrow (\sim r \wedge \sim p)$

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The translation was initiated by John Arras on 2001-10-10

John Arras
2001-10-10