Here is a single python statement that solves the problem:

    print([
        q for q in itertools.product((True, False), repeat=6)
        if q == (
            all(q[1:]),  # 1. All of the below.
            not any(q[2:]),  # 2. None of the below.
            all(q[:2]),  # 3. All of the above.
            any(q[:3]),  # 4. One of the above.
            not any(q[:4]),  # 5. None of the above.
            not any(q[:5]),  # 6. None of the above.
        )
    ])

A less clever solution, using the wonderful z3

  import z3
  answers = [z3.Bool(f"answer{i}") for i in range(1,7)]
  implications = [
      z3.And(answers[1:]),         # All of the below
      z3.Not(z3.Or(answers[2:])),  # None of the below
      z3.And(answers[:2]),         # All of the above
      z3.Or(answers[:3]),          # Any of the above
      z3.Not(z3.Or(answers[:4])),  # None of the above
      z3.Not(z3.Or(answers[:5]))]  # None of the above
  constraints = [z3.Implies(ans, impl) for ans,impl in zip(answers, implications)]
  z3.solve(constraints)

https://github.com/Z3Prover/z3