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Mathematics Senior High

集合と命題の問題なのですが、151番の(1)(2)(3) と152番の解き方が分かりません。どなたか分かる方解説してください!

110 151* (1) a,bは有理数とする。 √5 が無理数であることを用いて 命題 Ta+6√5=0→a=0かつb=0」を証明せよ。 &Oと仮定する。 このとき at&s=① を変形すると 15-0 Q.bは有理数であるから、①の右辺は有理数であり 等式①は厚が無理数であることに矛盾する したがってb:0 atb55=0にb=0を代入するとa=0 よって与えられた命題は真である (a+3)+(6-5)√5=0 を満たす有理数α, b の値を求めよ。 a,bが有理数ならば、a+3,65はともに有理数 である。よって(1)で証明したことから(a+3)+(b-5)55:0 を満たすとき a+3=0, b-5:0 ゆえに a=-3, b=5 (3) (√5-1)a+b/√5 = 2 + √5 を満たす有理数a, b の値を求めよ。 等式の左辺を展開して整理すると → 例題 38 (-a-2)+(a+b^-1)55=0 a,bが有理数ならば、-a-2,a+b-1はともに 有理数である。よって(1)で証明したことから、有理数a,bが (-a-2)+(a+b-1)55:0を満たすとき -a-2=0 a+b-1=0 ゆえに b=3 BClear a=-2 152x, y, z は実数とする。 次の命題を証明せよ。 x2 >yz かつye<xzならば, xキリである。 xyzかつy<xzならばx=yであると仮定する xyzにx=y を代入すると y² > YZ O y2<xzにx=y を代入すると y² < YZ.. ①と②は矛盾する よってxxかつくってならばメキまである

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English Senior High

3枚目の問いの答えを教えてください。 よろしくお願い致します。

Radio Host: durlar aind Roger Ali: Radio Host: Roger Ali: Radio Host: Roger Ali: Radio Host: Roger Ali: Roger Ali: Radio Host: Roger Ali: Radio Host: Welcome back. As I mentioned before the break, Roger Ali is with us today to talk about artificial intelligence. Thank you for being here, Dr. Ali. Thank you for having me. I'll be honest with you. When I hear the words "artificial intelligence," the first thing I think of is the character HAL from the movie 2001: A Space Odyssey. ch tud goons bad Radio Host:ome In other words, the search engine draws conclusions about what we're looking for on the Internet. Roger Ali: Sure. Many people remember HAL. In the movie, he's the computer that controls the systems of a spacecraft. He also speaks with the people on the spacecraft. And he's not very happy when the people decide to turn off the computer. In the movie, HAL becomes very dangerous. That's right, but fortunately, artificial intelligence in the real world isn't like HAL. Well, that's good! Can you tell us what is happening in the field of AI? Many interesting things. For example, when we search for something on the Internet, the search results that we see are chosen carefully. The search engine has learned which websites are the most popular, the most reliable, and so on. This prevents us from seeing a lot of websites we're not really interested in. Tosa Right, so it only shows us the information it thinks we want to see, which includes go advertisements as well. We usually see only ads for products that the computer thinks we might want to buy. You said, "It thinks," but is the search engine really thinking? IST That depends on your definition of thinking. The search engine is capable of learning machine learning-and it does have knowledge. Knowledge about the Internet. Are learning and knowledge part of your definition of thinking? They're part of it, but human beings are capable of so much more. We have our senses hearing, smell, sight, touch, taste-and our emotions. We notice a lot about the world, and we use our judgment to make decisions. That's true, and most computer scientists know that we can't replace human beings with computers. We don't intend to make robots for every kind of job, either. That's just not practical.

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