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 (A), X=1 (B), X∨X=X (D)</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 (B), X∧(X∨Y)=X (C)</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

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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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