Correct : b

The correct answer is Option B — a · a'' = 1, which is NOT a property of Boolean Algebra.
Option A — a + b = b + a: This is the Commutative Law for the OR operation — the order of operands does not affect the result. This is a valid Boolean Algebra property. Is a property.
Option B — a · a'' = 1: This is incorrect. The correct Complement Law for AND states that a · a'' = 0 — any variable ANDed with its own complement always equals 0, because one of them must be 0 and 0 AND anything = 0. The value 1 would require both a and a'' to be 1 simultaneously, which is impossible. NOT a property — Correct answer.
Option C — a + a'' = 1: This is the Complement Law for OR — any variable ORed with its complement always equals 1, since one of them must be 1. This is a valid Boolean Algebra property. Is a property.
Option D — a × b = b · a: Both × and · represent the AND operation here. This states the Commutative Law for AND — order of operands does not matter. This is a valid Boolean Algebra property. Is a property.