List and explain bolleen algebra laws

This law states that the order of operands does not affect the result of an operation.

• For ORing: $A + B = B + A$
• For ANDing: $A \cdot B = B \cdot A$

This law states that the grouping of operands does not affect the result of an operation when performing the same operation multiple times.

• For ORing: $(A + B) + C = A + (B + C)$
• For ANDing: $(A \cdot B) \cdot C = A \cdot (B \cdot C)$

This law describes how operations interact with each other, allowing for the expansion or factorization of Boolean expressions.

• $A \cdot (B + C) = (A \cdot B) + (A \cdot C)$
• $A + (B \cdot C) = (A + B) \cdot (A + C)$

This law defines the identity elements for OR and AND operations.

• For ORing: $A + 0 = A$
• For ANDing: $A \cdot 1 = A$

This law states that an element combined with its complement results in either the identity element for the other operation or the universal element.

• For ORing: $A + \bar{A} = 1$
• For ANDing: $A \cdot \bar{A} = 0$

This law states that performing an operation on an element with itself yields the same element.

• For ORing: $A + A = A$
• For ANDing: $A \cdot A = A$

This law allows for the simplification of expressions where one term "absorbs" another.

• $A + (A \cdot B) = A$
• $A \cdot (A + B) = A$
• A useful variation: $A + \bar{A}B = A + B$

These theorems provide rules for negating complex Boolean expressions.

• $\overline{A + B} = \bar{A} \cdot \bar{B}$
• $\overline{A \cdot B} = \bar{A} + \bar{B}$