Final answer:
The laws of Boolean algebra upon which the given equalities are based are the commutative law, distributive law, associative law, and identity law.
Step-by-step explanation:
The law of Boolean algebra that each of the following equalities is based on are:
a) Commutative Law: This law states that the order of the operands in a logical expression does not affect its outcome. For example, A + B = B + A
b) Distributive Law: This law states that a logical expression can be expanded by distributing a common factor across different terms. For example, A(B + C) = AB + AC
c) Associative Law: This law states that the grouping of operands in a logical expression does not affect its outcome. For example, (A * B) * C = A * (B * C)
d) Identity Law: This law states that an operand combined with its identity element equals itself. For example, A + 0 = A