Does the sentence "For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem." provide a valid answer to the question "How did von Neumann raise the level of economics?"

A: no

Does the sentence "Puerto Rico was able to maintain its Spanish language, culture, and identity because the relatively small, densely populated island was already home to nearly a million people at the time of the U.S. takeover, all of those spoke Spanish, and the territory was never hit with a massive influx of millions of English speakers like the vast territory acquired from Mexico 50 years earlier." provide a valid answer to the question "Was English in Puerto Rico successful?"

A: no

Does the sentence "On 3 July, two days after Francis's death sentence was commuted to transportation for life, John William Bean also tried to fire a pistol at the Queen, but it was loaded only with paper and tobacco and had too little charge." provide a valid answer to the question "What person recieved a seven year transportation sentence for striking Victoria on the head with his cane?"

A: no

Does the sentence "Influences on his compositional style include Polish folk music, the classical tradition of J. S. Bach, Mozart and Schubert, the music of all of whom he admired, as well as the Paris salons where he was a frequent guest." provide a valid answer to the question "What three composers influenced Chopin's work?"

A:
yes