Questions and Answers
What does A or A equal?
What does A and A equal?
What does A or B equal?
What does A and B equal?
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What does A or (B or C) equal?
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What does A and (B and C) equal?
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What does A and (B or C) equal?
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What does A or (B and C) equal?
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What does A or true equal?
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What does A and false equal?
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What does A and (A or B) equal?
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What does A or (A and B) equal?
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What does A and true equal?
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What does A or false equal?
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What does !(!A) equal?
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What does A or !A equal?
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What does A and !A equal?
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What does !(A or B) equal?
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Study Notes
Laws of Boolean Algebra
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Idempotent Laws:
- A or A = A: Repeating an operand in an OR condition does not change the outcome.
- A and A = A: Repeating an operand in an AND condition retains the operand.
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Commutative Laws:
- A or B = B or A: Order of operands does not affect the result in OR operations.
- A and B = B and A: Order of operands does not affect the result in AND operations.
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Associative Laws:
- A or (B or C) = (A or B) or C: Grouping in OR operations does not affect the outcome.
- A and (B and C) = (A and B) and C: Grouping in AND operations remains unchanged.
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Distributive Laws:
- A and (B or C) = (A and B) or (A and C): AND distributes over OR.
- A or (B and C) = (A or B) and (A or C): OR distributes over AND.
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Laws of Union and Intersection:
- A or true = true: Any operand ORed with true results in true.
- A and false = false: Any operand ANDed with false results in false.
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Law of Absorption:
- A and (A or B) = A: An AND operation absorbs ORed terms if one of the operands is the first term.
- A or (A and B) = A: An OR operation absorbs ANDed terms if one of the operands is the first term.
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Identity Elements:
- A and true = A: True acts as the identity element in AND operations.
- A or false = A: False acts as the identity element in OR operations.
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Double Negative Law:
- !(!A) = A: Negating a negation returns the original operand.
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Complement Laws:
- A or !A = true: An operand ORed with its complement results in true.
- A and !A = false: An operand ANDed with its complement results in false.
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DeMorgan's Laws:
- !(A or B) = !A and !B: The negation of an OR statement becomes the AND of their negations.
- !(A and B) = !A or !B: The negation of an AND statement becomes the OR of their negations.
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Description
Explore the fundamental laws of Boolean algebra through a series of flashcards. This quiz covers key concepts like the idempotent, commutative, and associative laws for both 'or' and 'and' operations. Perfect for students looking to enhance their understanding of logic in mathematics and computer science.
