Boolean Algebra Laws

Question 1

What is the Commutative law for addition?

Answer 1

A + B = B + A

This law states that the order of addition does not affect the result.

Question 2

What is the Commutative law for multiplication?

Answer 2

A. B = B. A

This law indicates that the order of multiplication does not affect the result.

Question 3

What does the identity law state for AND?

Answer 3

A. A = A

This law indicates that a variable ANDed with itself equals the variable.

Question 4

What does the identity law state for OR?

Answer 4

0 + A = A

This law indicates that false ORed with a variable equals the variable.

Question 5

What is the result of ANDing a variable with false?

Answer 5

0. A = 0

This indicates that any variable ANDed with false results in false.

Question 6

What is the result of ORing a variable with true?

Answer 6

1 + A = 1

This indicates that any variable ORed with true results in true.

Question 7

What is the result of ORing a variable with itself?

Answer 7

A + A = A

This indicates that ORing a variable with itself results in the variable.

Question 8

What is the result of ORing a variable with its negation?

Answer 8

A + A = 1

This indicates that ORing a variable with itself results in true.

Question 9

What does the Associative law state for multiplication?

Answer 9

(A. B). C = A. (B. C)

This law indicates that the grouping of variables does not affect the result of multiplication.

Question 10

What does the Associative law state for addition?

Answer 10

(A + B) + C = A + (B + C)

This law indicates that the grouping of variables does not affect the result of addition.

Question 11

What does the Distributive law state?

Answer 11

A. (B + C) = A. B + A. C

This law indicates that a variable ANDed with a sum is equal to the sum of that variable ANDed with each term.

Question 12

What is the result of ANDing a variable with a sum of itself?

Answer 12

(A + B). (A + B) = A.A + B.B + A. B + A. B

This shows the expansion of ANDing a sum.

Question 13

What is the absorption law for OR?

Answer 13

A + A. B = A

This law indicates that ORing a variable with itself ANDed with another variable results in the original variable.

Question 14

What is the absorption law for AND?

Answer 14

A. (A + B) = A

This law indicates that ANDing a variable with itself ORed with another variable results in the original variable.

Question 15

What does De Morgan’s law state?

Answer 15

Ã. B = A + B

This law relates the complement of a product to the sum of the complements.

Question 16

What is the result of ORing a variable with its AND?

Answer 16

A + B = A. B

This indicates a relationship between OR and AND operations.