Given a set X N, define

X^e={nX | n is even}

and

X^o={nX | n is odd}

Denote by E the set of all even numbers in N and by O the set of all odd numbers in N. Function f₇: P(N) P(E) P(O) is defined by

f₇(X) = X^e, X^o.

Determine whether the function is injective and surjective