Boolean Algebra Rules Flashcards

Questions and Answers

What is the Commutative Law for conjunction in Boolean algebra?

A ˅ B = B ˅ A (correct)

A ^ B = B ^ A (correct)

A ^ (B ˅ C) = (A ^ B) ˅ (A ^ C)

A ˅ (B ˅ C) = (A ˅ B) ˅ C

What does the Associative Law state for conjunction?

A ˅ (B ˅ C) = (A ˅ B) ˅ C (correct)

A ^ B = B ^ A

A ˅ A = A

A ^ (B ^ C) = (A ^ B) ^ C (correct)

Which of the following is part of the Distributive Law?

A ˅ ¬A = T

A ^ (B ˅ C) = (A ^ B) ˅ (A ^ C) (correct)

A ^ A = A

A ˅ (B ^ C) = (A ˅ B) ^ (A ˅ C) (correct)

What do Idempotent Laws state in Boolean algebra?

A ^ A = A Signup and view all the answers

What does the Identity Law for conjunction state?

A ˅ (A ^ B) = A Signup and view all the answers

What do the Complement Laws state?

A ˅ ¬A = T Signup and view all the answers

What does the Involution Law state?

¬(¬A) = A Signup and view all the answers

Which of the following is part of DeMorgan's Laws?

¬(A ˅ B) = (¬A) ^ (¬B) Signup and view all the answers

Study Notes

Commutative Laws

States that the order of operands does not affect the result.
For AND operation: A ^ B = B ^ A.
For OR operation: A ˅ B = B ˅ A.

Associative Laws

Indicates that how operands are grouped does not change the outcome.
For AND operation: A ^ (B ^ C) = (A ^ B) ^ C.
For OR operation: A ˅ (B ˅ C) = (A ˅ B) ˅ C.

Distributive Laws

Demonstrates how AND and OR operations can distribute over each other.
For AND over OR: A ^ (B ˅ C) = (A ^ B) ˅ (A ^ C).
For OR over AND: A ˅ (B ^ C) = (A ˅ B) ^ (A ˅ C).

Idempotent Laws

Show that applying the same operation multiple times yields no change in result.
For AND operation: A ^ A = A.
For OR operation: A ˅ A = A.

Identity Laws

Define how identities for AND and OR do not alter the operand.
For AND operation: A ^ (A ˅ B) = A.
For OR operation: A ˅ (A ^ B) = A.

Complement Laws

Relate an operand with its complement to produce constant results.
For AND operation: A ^ ¬A = F (false).
For OR operation: A ˅ ¬A = T (true).

Involution Law

Explores the effect of double negation.
States that negating a negation returns the original value: ¬(¬A) = A.

DeMorgan's Laws

Transforms expressions involving negations of AND and OR operations.
Negation of AND: ¬(A ^ B) = (¬A) ˅ (¬B).
Negation of OR: ¬(A ˅ B) = (¬A) ^ (¬B).

Description

Explore the fundamental rules of Boolean Algebra with these flashcards. Each card presents a key rule, such as Commutative, Associative, and Distributive Laws, along with their definitions. Perfect for quick reviews and enhancing your understanding of Boolean logic.