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Questions and Answers
What is the Commutative Law for conjunction in Boolean algebra?
What is the Commutative Law for conjunction in Boolean algebra?
- A Ë… B = B Ë… A (correct)
- A ^ B = B ^ A (correct)
- A ^ (B Ë… C) = (A ^ B) Ë… (A ^ C)
- A Ë… (B Ë… C) = (A Ë… B) Ë… C
What does the Associative Law state for conjunction?
What does the Associative Law state for conjunction?
- A Ë… (B Ë… C) = (A Ë… B) Ë… C (correct)
- A ^ B = B ^ A
- A Ë… A = A
- A ^ (B ^ C) = (A ^ B) ^ C (correct)
Which of the following is part of the Distributive Law?
Which of the following is part of the Distributive Law?
- A ˅ ¬A = T
- A ^ (B Ë… C) = (A ^ B) Ë… (A ^ C) (correct)
- A ^ A = A
- A Ë… (B ^ C) = (A Ë… B) ^ (A Ë… C) (correct)
What do Idempotent Laws state in Boolean algebra?
What do Idempotent Laws state in Boolean algebra?
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What does the Identity Law for conjunction state?
What does the Identity Law for conjunction state?
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What do the Complement Laws state?
What do the Complement Laws state?
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What does the Involution Law state?
What does the Involution Law state?
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Which of the following is part of DeMorgan's Laws?
Which of the following is part of DeMorgan's Laws?
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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 Ë… B = B Ë… 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 Ë… (B Ë… C) = (A Ë… B) Ë… C.
Distributive Laws
- Demonstrates how AND and OR operations can distribute over each other.
- For AND over OR: A ^ (B Ë… C) = (A ^ B) Ë… (A ^ C).
- For OR over AND: A Ë… (B ^ C) = (A Ë… B) ^ (A Ë… 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 Ë… A = A.
Identity Laws
- Define how identities for AND and OR do not alter the operand.
- For AND operation: A ^ (A Ë… B) = A.
- For OR operation: A Ë… (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).
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