1 578 NO
If planet x has a diameter n slightly larger than the diameter m of planet y, then n is greater than m. From t, we know that Io, a planet, has a diameter of 3598 kilometers. We also know from t that Io has a diameter that is slightly larger than that of Earth's moon. Therefore, Io has a diameter that is greater than the diameter of Earth's moon. Since the terrestrial moon is Earth's moon, we know from h that Earth's moon has a diameter of 3746. Therefore, we can deduce that 3598 is greater than 3746. But it's not the case that 3598 is greater than 3746. We have thus arrived at a contradiction. QED
2 227 YES
Alison Hargreaves (who we can denote by 'a') has a number of attributes, according to the given proposition. For example, we can immediately deduce that a is a woman, and that a climbed Mount Everest (which we can denote by 'e') alone. Given that if x climbed y alone, x climbed y solo, we can deduce that a climbed e solo. Given as well that if x climbed y solo, x succeeds in climbing y solo, we can deduce that a succeeds in climbing e solo. By generalization, we can now deduce that there exists an x such that x is a woman, and x succeeds in climbing e solo. QED
3 286 YES
It follows immediately from the first sentence in the premise that the following conjunction holds: Fellini was Italian, was a film-maker, and was awarded an honorary Oscar. Since from any conjunction each of the elements conjoined can be inferred, it can be inferred in this case that Fellini was a film-maker. Since if x is a film-maker, x is a director, it follows that Fellini was a director. Assembling a new conjunction, we can deduce that Fellini was Italian, was a director, and was awarded an honorary Oscar. Generalizing, we can from this deduce that an Italian director was awarded an honorary Oscar. QED
4 70 YES
We can deduce from the premise that Hughes loved his wife, Gracia. (This is just one of the two conjuncts in the premise, after all.) We know that if x loved y, where y is the wife of x, then y was the wife of x. We can therefore deduce that Gracia was the wife of Hughes. We also know that if x was the wife of y, then y was married to x. Thus we can deduce that Hughes was married to Gracia. QED
5 581 YES
We know from t that Stephen Jay Gould has made guest appearances on the show, that Stephen Hawking has made guest appearances on the show, that Stephen Hawking is a theoretical physicist, and that Stephen Hawking's brilliance has been compared with Einstein's. It follows that Stephen Hawking is a theoretical physicist. If x is a theoretical physicist, x is a physicist. Therefore, Stephen Hawking is a physicist. QED
6 570 YES
From t we know that President Bill Clinton on Tuesday passed the leadership of the Democratic Party to Vice President Al Gore, and that Bill Clinton described his deputy as the right person to be the first U.S. President of the 21st century. If person x on day D passes the leadership of a political party P to person y, x belongs to P. Therefore, Bill Clinton belongs to the Democratic Party. QED
7 550 YES
From t we know that Bukowski attracted the attention of John Martin, and that John Martin founded Black Sparrow Press in 1965, and that John Martin founded Black Sparrow Press in 1965 in order to publish Bukowski. It follows directly from the second of these conjuncts that John Martin founded Black Sparrow Press in 1965. If x founded an organization O in year n, then x is the founder of O. It follows that John Martin is the founder of Black Sparrow Press. QED
8 470 YES
From t we know that Gabriel Garcia Marquez is the author of the novel ``One Hundred Years of Solitude,'' is the author of the novel ``The Autumn of the Patriach,'' and is the author of at least two additional novels. We can directly infer that Gabriel Garcia Marquez is the author of the novel ``One Hundred Years of Solitude.'' If x is the author of the novel b, then x is a novelist and writer. It follows that Gabriel Garcia Marquez is a novelist and writer. QED
9 452 YES
From the second sentence of t we can deduce that Boris Becker won Wimbledon at 17 years of age, and that Boris Becker went on to become the most prolific tennis player. If x won Wimbledon at n years of age, then x is a Wimbleton champion. Therefore, Boris Becker is a Wimbledon champion. QED
10 455 YES
If x was n years of age when e occurred (month day year), then in year, event e occurred. From the second sentence of t, and this rule, it follows that in 1945, the atomic bomb was dropped on Hiroshima. We know that if the atomic bomb was dropped on X, an atomic bomb was dropped on X. It follows that in 1945, an atomic bomb was dropped on Hiroshima. QED