Logic Laws and Operations Quiz

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)

X∨0=X Signup and view all the answers

What is the Rule of NOT?

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

What does the commutative law state?

X∧Y = Y∧X OR X∨Y = Y∨X Signup and view all the answers

What does the associative law state?

X∧(Y∧Z) = (X∧Y)∧Z OR X∨(Y∨Z) = (X∨Y)∨Z Signup and view all the answers

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

X∨(X∧Y)=X Signup and view all the answers

What is the Distributive Law?

X∧(Y∨Z) = (X∧Y)∨(X∧Z) OR X∨(Y∧Z) = (X∨Y)∧(X∨Z) Signup and view all the answers

What is the Double Negative rule?

X = ¬¬X 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

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.