Consider the following premises. For all x_10, if x_10 listens to a song, then x_10 is a politician. For all x_10, if x_10 plays a game, then x_10 is listening to a song. For all x_10, x_10 is not a politician. Jennifer is playing a game or it is cloudy. Can we infer the following from them? It is not raining.
We cannot infer that from the premises. Therefore the answer is no.