Practice Theorem 5 (commutative Laws) (6.3.5) - Boolean Algebra and Simplification Techniques - Part A
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Theorem 5 (Commutative Laws)

Practice - Theorem 5 (Commutative Laws)

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Is it true that A + B equals B + A? Explain why.

💡 Hint: Think about how changing the order affects the outcome.

Question 2 Easy

What is the expression for B · A?

💡 Hint: Use the property we just learned.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What are the two main statements of the Commutative Laws in Boolean algebra?

A + B = B + A and A · B = B · A
A · B = C and A + B = C
A + A = A and A · A = A

💡 Hint: Focus on how order relates to outcome.

Question 2

True or False: The equation A · B = B · A illustrates the application of the Commutative Law.

True
False

💡 Hint: Think of how operators work.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Design a Boolean circuit using the commutative property to prove that the input sequence can be interchanged without changing the output.

💡 Hint: Diagram it out and think of logical equivalences.

Challenge 2 Hard

Given a complex boolean expression involving multiple variables, how would rearranging terms make it easier to simplify?

💡 Hint: Look for opportunities to combine like terms.

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Reference links

Supplementary resources to enhance your learning experience.