Logic Laws and Operations Quiz
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Questions and Answers

What is A∧B equal to?

¬(¬A∨¬B)

What is A∨B equal to?

¬(¬A∧¬B)

Which of the following are Rules of AND? (Select all that apply)

  • X∧1=X (correct)
  • X∧0=1
  • X∧X=X (correct)
  • X∧¬X=0 (correct)
  • Which of the following are Rules of OR? (Select all that apply)

    <p>X∨0=X</p> Signup and view all the answers

    What is the Rule of NOT?

    <p>¬(¬X)=X</p> Signup and view all the answers

    What does the commutative law state?

    <p>X∧Y = Y∧X OR X∨Y = Y∨X</p> Signup and view all the answers

    What does the associative law state?

    <p>X∧(Y∧Z) = (X∧Y)∧Z OR X∨(Y∨Z) = (X∨Y)∨Z</p> Signup and view all the answers

    Which of the following are true according to the Redundancy Law? (Select all that apply)

    <p>X∨(X∧Y)=X</p> Signup and view all the answers

    What is the Distributive Law?

    <p>X∧(Y∨Z) = (X∧Y)∨(X∧Z) OR X∨(Y∧Z) = (X∨Y)∧(X∨Z)</p> Signup and view all the answers

    What is the Double Negative rule?

    <p>X = ¬¬X</p> Signup and view all the answers

    Study Notes

    DeMorgan's Law

    • A∧B is equivalent to ¬(¬A∨¬B)
    • A∨B is equivalent to ¬(¬A∧¬B)

    Rules of AND

    • Anything ANDed with 1 retains its original value: X∧1=X
    • Anything ANDed with 0 results in False: X∧0=0
    • Anything ANDed with itself results in itself: X∧X=X
    • Any variable ANDed with its inverse is always False: X∧¬X=0

    Rules of OR

    • Anything ORed with 1 is always True: X∨1=1
    • Anything ORed with 0 retains its original value: X∨0=X
    • Anything ORed with itself results in itself: X∨X=X
    • Any variable ORed with its inverse is always True: X=1

    Rule of NOT

    • Applying NOT twice returns the original value: ¬(¬X)=X

    Commutative Law

    • AND operation is commutative: X∧Y = Y∧X
    • OR operation is commutative: X∨Y = Y∨X

    Associative Law

    • AND operation is associative: X∧(Y∧Z) = (X∧Y)∧Z
    • OR operation is associative: X∨(Y∨Z) = (X∨Y)∨Z

    Redundancy Law

    • X∨(X∧Y) simplifies to X
    • X∧(X∨Y) simplifies to X

    Distributive Law

    • AND distributes over OR: X∧(Y∨Z) = (X∧Y)∨(X∧Z)
    • OR distributes over AND: X∨(Y∧Z) = (X∨Y)∧(X∨Z)

    Double Negative

    • Applying NOT twice yields the original value: X = ¬¬X

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    Description

    Test your knowledge on DeMorgan's Law, rules of AND, OR, and NOT, as well as the Commutative, Associative, Redundancy, and Distributive Laws. This quiz will challenge your understanding of logical operations and their properties. Perfect for students learning foundational logic in mathematics or computer science.

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