Lecture 4 Problem Discussion Notes

Overview

• Discussion of problems associated with Lecture 4.
• Focus on simplifying Boolean expressions and determining equivalent expressions.

Problems

Problem 4.1

• Expression to simplify:
  • A'B or C or D AND A'B or D
• Choices for equivalent expressions:
  • Choice A: A' or D
  • Choice B: B or D
  • Choice C: A'B
  • Choice D: A'B or D
• Task: Choose the expression that is always equal to the given expression for any values of Boolean variables.

Problem 4.2

• Expression to simplify:
  • A' or B or C' AND A' or C' or D AND B' or D'
• Choices for equivalent expressions:
  • Choice A: A' or C' AND B' or D'
  • Choice B: A or C AND B or D
  • Choice C: A' or D' AND B' or C'
  • Choice D: A' or C AND B' or D
• Task: Choose the expression that is always equal to the given expression for any values of Boolean variables.

Hints and Approaches

• Simplification:
  • Use simplification techniques and theorems discussed in the lecture to solve these problems.
• Truth Tables:
  • Two expressions are equivalent if and only if they have the same truth table.
  • Constructing truth tables is a valid approach but may be tedious.
  • Prefer simplification and multiplication of expressions to find equivalence.

Conclusion

• Attempt to solve by simplification first and use truth tables as a secondary method if needed.
• Apply knowledge from the lecture to approach these problems effectively.