input: Write a function to implement a basic machine learning model in Python that performs binary classification on the given data. The function should use sklearn's LogisticRegression model and return the accuracy of the model on the provided data. The function should be able to handle the input and output as described below.
  assert binary_classifier([[0.3, 0.2, 0.6], [0.3, 0.1, 0.4], [0.2, 0.3, 0.4], [0.7, 0.4, 0.2], [0.5, 0.2, 0.1]], [1, 0, 0, 1, 0])==1.0
  assert binary_classifier([[0.5, 0.4, 0.1], [0.3, 0.2, 0.5], [0.1, 0.7, 0.2], [0.9, 0.1, 0.0]], [1, 1, 0, 0])==0.75
  assert binary_classifier([], [])==None
  assert binary_classifier([[0.2, 0.2, 0.2]], [0])==1.0
output: def binary_classifier(X, y):
      if not X or not y:
          return None
      model = LogisticRegression()
      model.fit(X, y)
      return model.score(X, y)