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数学 高校生

数学1aの数と式の問題です。 黄色マーカーで引いたところがよく分かりません。 なぜそう言えるのでしょうか?

基礎問 42 第1章 数と式 23 命題の真偽 (1) 命題: x≧1 かつ y≧1 ならば, x+y≧2 について 逆・裏・対偶を述べ,その真偽を調べよ. (2)命題:キならばェキ1が正しいことを対偶を用いて 明せよ. (B)√2が無理数であることを背理法を用いて示せ。 精講 (1), (2) ある命題が正しいことを真 (true), 間違っていることを偽 (false) といいます. また, 次表のような関係にある命題を、 それ ぞれ,元の命題の逆裏 対偶といいます(→は 「ならば」を意 味します). → g 裏 p-q 対偶 解答 (1) 逆:x+y≧2 ならば, x≧1 かつ y≧1 x=2, y=0 のとき, 不成立だから偽 g→p 逆 (万はかの否定を表す) このとき, 対偶の関係にある2つの命題の真偽は一致します. (3) 「背理法」という証明の手段は, 次の手順ですすみます. Ⅰ. 結論を否定して議論を開始し ⅡI. その結果, 矛盾が生じる ⅢI.だから、結論を否定したものは誤りで、要求された事実は正しい 裏x<1または y<1 ならば, x+y<2 x=2,y=0 のとき, 不成立だから 偽 裏 9 p 偽であることを示す には不適当な例(= 反例)を1つあげれ ばよい <かつq または 対偶:x+y<2 ならば、 x<1まだは y<1 もとの命題が真だから, 対偶も真 (2)与えられた命題の対隅は 「z=1ならば よって、与えられた命題 「キならばキ1」は真. 注 対偶を用いて証明する場合は、たいてい 「キ」 「または」, 「ある ...... に対して」 という表現が含まれています。 (3) √2が有理数と仮定すると, これは真. '=x」で, ポイント m 2つの自然数m,n を用いて√2=1 と表せる. (ただし, m, nは互いに素) 両辺を平方すると2m²=n2 左辺は偶数だから,n² も偶数 すなわち, nも偶数. このとき,n24の倍数だから, 2m²も4の倍数. よって, m² は偶数となり, mも偶数. ゆえに、mとnは共通の約数2をもつことになり、 mとnが互いに素であることに矛盾する. よって,√2は有理数ではない. すなわち √2は無理数. 演習問題 23 43 まず、 結論の否定 最大のポイント 背理法では結論を否定して解答をかき始め、 その結果, 矛盾することを示す 第1章 (1) 命題: 0<x<1 ならばx" <1 について 逆, , 対偶を述べ、その真偽を調べよ. (2) 命題: xy≠2 ならば r≠1 またはy=2 が正しいことを対偶 を用いて証明せよ。 (3)√2が無理数であることを用いて,√2+1 も無理数であるこ とを背理法で証明せよ.

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英語 高校生

この解答を教えていただきたいです。

Speed Reading The rainforest is not the only place where animals are How Can We Save Endangered Species? In the modern world, many animals die from causes that are not natural. the species living in the rainforest. Every day, more and more areas of rainfore are cut down or burned, and all of the animals living there lose their habitat. and dying. Around cities, animals are facing similar situations. As cities humans move into the natural areas surrounding them. This means that animal living near humans must move to other areas. Those animals-or in some cases those species-which are not able to adapt or to find new homes eventually die. In recent years, efforts have been made to protect certain lands in order to prevent killing plant and animal species native to the area. State and national parks along with special areas for birds and wildlife, have been established to protect the natural homes of endangered species. Also, wildlife management programs have helped bring back some species from almost certain extinction. For example, fewer than 50 years ago, the North American bald eagle was in serious danger of extinction because too many farmers used DDT, a chemical that kills insects. Farmers stopped 10P 15 >> using DDT, and the bald eagle is no longer endangered today.m Although protected lands have been established and wildlife management programs keep an eye on highly endangered species, scientists have yet to determine if these efforts are enough. Is it possible to save all the plants and animals that are endangered today, or is it already too late? (259 words) da siqag 000 259 words ÷ ( ) seconds × 60 = () wpm ~99 wpm ---Beginner 100~149 wpm Intermediate 150 wpm ~ dvanced QAnswer T (true) or F (false). 1. In the modern world, animals living in the rainforest are losing their place to live. ( ) 2. Animals living around cities do not have the same problem as those living in the rainforest. 3. Animals which have lost their habitat near the cities cannot survive unless they can adapt or find new homes. () 4. People in the US saved bald eagles by not using DDT; this is an example of a successful wildlife management program. 5. Some scientists believe that wildlife management programs are not necessary () anymore. New words adapt /ədæpt/ wildlife/wáildlarf/ chemical/kémikal/ management /mænidzmant/ bald /bó:ld/ eagle/i:gl/ 24 Speed Reading insect/insekt/ Lesson Consi losing their home b i t

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英語 高校生

下の5問お願いします

Less Changing Behavior in Unique Ways Comprehension Can-Do Language 人々の行動を変え、社会を向上させる「仕掛け」の機能を理解することができる。 不定詞を適切に用いることができる。 人の行動を変えるだけを見てような方法があるでしょうか。柔軟な考えから生まれた。好ましい行動を促 ▶▶▶ Read the passage. Easy Version 197 words 目標1分58秒 There are some interesting ways to change people's behavior. If you draw a line on the backs of file boxes, people will know where to put them on the shelf. 行動 ファイルボックス If you put a basketball hoop above a toy box, children will want to put away their toys. These ways are ゴール ~を片付ける called triggers. 仕掛け There are other good examples of triggers: the “Piano Stairs” and “The World's Deepest The stairs make piano-like sounds when people use them. The bin makes an [ Bin. ピアノのような interesting sound when people put trash in it. These triggers come from new, flexible ideas. Such ideas are useful to deal with social problems. To make children wash their hands, soap ごみ 柔軟な that has a toy inside was used in South Africa. After the Great Hanshin-Awaji Earthquake, 南アフリカ共和国 阪神淡路大震災 volunteers used dekimasu zekken and showed their skills. Triggers to solve social problems are called social design. You can see it in many Japanese cities or villages. For example, Inakadate Village started to design rice fields as 田舎館村 art, and now many people visit the village. If people give money to Kumamoto Castle for its 熊本城 renovations, they can become "castle lords." In these ways, social design can make our 修復 城主 communities better. Answer T (True) or F (False). (1) Triggers are a good way to change people's behavior. ( :) (2) Both the "Piano Stairs" and "The World's Deepest Bin" make sounds when people use them. (3) Children in South Africa used toys when they washed their hands. (4) A lot of people go to Inakadate Village to visit an art museum. (5) For renovations, the lord of Kumamoto Castle collected money. ( Lesson 4 33 onal kodan-shi rmance : kodan-shi ly

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英語 高校生

これの解答を教えていただきたいです。

Lesson Language Revitalization in Hawaii Unfortunately, the beautiful native Hawaiian language has been endangered century, making English the language of choice. At first, the discovery of Hawaii by the West seemed to help the growth cince the early 19th century. In 1778. there were 500.000 native Hawaiian of the Hawaiian language. Western people wrote the Hawaiian language in the Roman alphabet, and Hawaiian-language newspapers were printed and cneakers. However, American and British influence grew in the following ger. Hourished because most of the native population had learned to read. It was a time of major cultural change for the native Hawaiian population. However, as more immigrants came to Hawaii from America, Europe, x X causng oW up lo be dhon theory was and financial power on the islands, many parents stopped speaking Hawaiia with their children. They saw English as the language of opportunity. Then a law was passed making English the official language in schools. Due to these Parents who of their baties. and Asia, and as American and British businessmen got increasing political heir parentd g jon over the o sick people va factors, the number of Hawaiian speakers fell to about 1,000 native speakers. In the 1970s, native Hawaiians began the revitalization of the Hawaiian che condhioimn language. In 1978, Hawaiian became one of the official state languages, along Chem! with English, and became a required course in Hawaiian schools. There has addition to the 1,000 native speakers, there are now about 8,000 people that can speak and understand the language. Aarere also been an increase in Hawaiian-language schools, with some students being taught in Hawaiian and many more learning it as a second language. Thus, in (245 words) ) seconds × 60 = ( )wpm 150 wpm~… .@Advanced 245 words -( 100~149 wpm…OIntermediate -@Beginner ~99 wpm … grown.() npa Q Answer T (true) or F (false). nA of B. 3. Even though Hawaiian-language newspapers were printed, most of the Hawaiian people could not read them. 1. People in Hawaii chose English because American and British influence had 2. At first, Western people helped the Hawaiian language grow. 5. People in Hawaii have succeeded in revitalizing the Hawaiian language.() alphabet /elfabet 4. The Hawaiian language was the language of opportunity for immigrants. ( ) Hawaiian /howá:jan/ choice /tóis/n growth /gróu0/ businessmen /biznasmèn/ (<businessman) New words political /palitikal/ Hawaii /hawá:i:/ Speed Readin print /prinl/ immigrant /imigrant/ financial /fondenjal, far-/ Sads h mons Jooks like woverlookng anen and B. Theresloe, hey grow oldor, a

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英語 高校生

合ってるか見てほしいです!お願いします

不定詞·動名詞の基本を理解して文を作る)次の文を英語にしなさい。 4 Hints 4 )映画館では,携帯電話の電源を切ることが求められている。 (1) 32 (電源など)を切る turn (~) off (2)私は保育所で乳幼児の世話をするボランティア活動をすることにした。 (2) 33, 34 (3)重要なことは私たちに間違った情報を見抜く能力があるかどうかということだ。 (3) 34 ~を見抜く 【札幌大) detect d= (4)マナーを身につけるとは,他人に目をやって,他人を思いやることである。 (4) 32 [大阪薬科大) +2)= [J ) ひんばん (5)友だちと一緒にいるときは,スマートフォンで頻繁にメールをチェックすること によって友だちの気分を害することがないように気をつけよう。 (5) 35 (中央大) bummy 対の の( Toddd vm lob Plus 目的語に動名詞をとるか, 不定詞をとるか。 ●動名詞だけを目的語にとる頻出動詞(句) admit, deny, finish, give up, stop, enjoy, practice, avoid, escape, mind, miss, postpone, put off, consider, imagine, suggest ●不定詞だけを目的語にとる頻出動詞 claim, decide, demand, desire, determine, expect, hope, manage, mean, offer, plan, promise, pretend, refuse, wish, want ●目的語に動名詞をとるか,不定詞をとるかによって意味が大きく異なる動詞 remember, forget, regret, try 不定詞。動名詞(1) 45

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