Complex Conditions Direct Answer Kate Deibel March 29, 2004 Direct Answer

Instructors can find out if students can apply De Morgan's laws correctly to conditionals.

Please simplify the following conditionals so that the ! operator is only used as !=. As you complete these problems, keep in mind De Morgan's laws. Here A and B represent integer variables.

  1. !(A != B)
  2. !((A <= B))
  3. !((A == 1) || (A == 4))
  4. !((A >= 4) && (B < 2))
  5. !((A <= 5) || (B == 6))
  6. !((A != 5) || (A == 5))
  7. !((A != 5) && (A == 5))
  8. !((A > B) || !(A == B))
  1. (A == B)
  2. (A > B)
  3. (A != 1) && (A != 4)
  4. (A < 4) || (B >= 2)
  5. (A > 5) && (B != 6)
  6. (A == 5) && (A != 5) become false
  7. (A == 5) || (A != 5) becomes true
  8. (A <= B) && (A == B) becomes (A == B)

The following must be done out of class:

  1. In a first pass, mark and count the number of incorrect answers.
  2. 2. For each question that has a significant (your judgement call) of incorrect answers, do the following:
    1. Look through the answers to these questions.
    2. Place different incorrect answers in separate piles.
    3. Attempt to identify the nature of the most common errors that are made.
  3. Discuss in class these errors in class, using the common mistakes that you identified.

In-class feedback can be done by having students write their own answers, but caution must be taken to avoid embarassing or ridiculing a student for making mistakes.

Have students work in groups to complete this activity. The instructor may want to circulate throughout the groups to ensure that each group is making progress. After the groups have completed the problems, the instructor can ask for volunteers for each problem. Be sure to ask for explanations of the arithmetic. Have students work individually on their problems and form a small group to discuss their answers. Have each group give their answer to the rest of the class and encourage them to describe the laws they used to find their answer. Develop problem-solving skills Improve mathematical skills Learn terms and facts Learn concepts and theories Improve skills at paying attention De Morgan's law Booleans Logic Logical Operators Negation Expressions Conditionals MEDIUM MEDIUM LOW LOW Lecture Next Day Summary Class Discussion Small Group Discussions Homework Could be Enabled Mathematics Types