Question: According to the theorem on finite Boolean algebras, which we did not prove, any finite Boolean algebra must have 2m elements for some m. Prove the weaker statement that no Boolean algebra can have an odd number of elements. (Note that in the definition of a Boolean algebra, 0 and 1 are distinct elements of B, so B has at least two elements. Arrange the remaining elements of B so that each element is paired with its complement.)