Assessment Tool

Lecture 11: Complex Conditions

Content Tested: Application of De Morgan's laws

Lecture Content:

Complex conditions
Boolean operators
Negating a condition
Truth tables
De Morgan's laws

Goals:

Develop ability to apply principles and generalizations already learned to new problems and situations
Develop problem-solving skills
Improve mathematical skills
Prepare for transfer or graduate study
Learn techniques and methods used to gain new knowledge in this subject

Assessment Technique: Simplifying Conditionals

Purpose:

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

Activity:

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 variables.

1. !(A != B)

2. !((A == 1) || (A == 4))

3. !((A >= 4) && (B < 2))

4. !((A != 5) || (B == 6))

5. !((A != 5) || (A == 5))
(Note: Can this conditional evaluate to true?)

6. !((A != 5) && (A == 5))
(Note: Can this conditional evaluate to false?)

Conditionals that never evaluate to true are called contradictions. Conditionals that always evaluate to true are called tautologies.

Possible Solutions

1. !(A != B)
A == B

2. !((A == 1) || (A == 4))
A != 1 && A != 4

3. !((A >= 4) && (B < 2))
A < 4 || B >= 2

4. !((A != 5) || (B == 6))
A == 5 && B != 6

5. !((A != 5) || (A == 5))
(Note: Can this conditional evaluate to true?)
A == 5 && A != 5
This conditional is always false.

6. !((A != 5) && (A == 5))
(Note: Can this conditional evaluate to false?)
A == 5 || A != 5
This conditional is always true.

Possible Uses of Activity:

Encourage students to work on these exercises alone and then consult with classmates about their solutions.
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.