(e)(4%) Can any Boolean function be represented in the exclusive-product-of-suns (EPOS) expression, which is the XOR-AND two-level expression (with first level XOR and second level AND)? Justify your answer.

(a) (10%) Prove by induction that it represents an odd-parity function, that is, it evaluates to 1 if and only if the assignment to variables X1,...,Xn contains an odd number of 1's. (For example, the assignment (X1, X2, X3, X4)= (1,0,0,0) contains one 1.)