Consider the following premises. For all x, x will read a book if and only if x is a politician. For all x, x will not read a book. Patricia is happy if and only if it is cold. For all x, x is a politician if and only if x is happy. Can we infer the following from them? It is not cold.
 From the fact that for all x, x will read a book if and only if x is a politician, and that for all x, x will not read a book we can infer that for all x, x is not a politician. From the fact that for all x, x is a politician if and only if x is happy, and that for all x, x is not a politician we can infer that for all x, x is not happy. From the fact that for all x, x is not happy we can infer that Patricia is not happy. Finally, from the fact that Patricia is happy if and only if it is cold, and that Patricia is not happy we can infer that it is not cold. Therefore, the answer is yes.