Can a contradiction Boolean expression with variables 𝑎 and 𝑏 be represented in NAND form?

Question

I have f(a,b) = 0 and want to represent it in NAND form (only using NAND gates) in terms of a and b, but I don't think is possible.

Answer 1

def NAND(a, b):
    return (a & b) ^ 1

def f(a, b):
    return NAND(
        NAND(a, NAND(a, a)),
        NAND(b, NAND(b, b)),
    )

for a in 0, 1:
    for b in 0, 1:
        print(f(a, b))

Output (Attempt This Online!):

0
0
0
0