Question

求解图片中的数学证明题

求解这几道题的证明 如果有因为语言看不懂 但会的 可以提问我哪里看不懂 再帮我解决问题 谢谢

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Answer 1

4(a)proof:
for every prime number p ,we have only one even number is 2,and others is all odd

case1: p is even,p=2 then p+7=9 is acomposite
case2 p is odd ,7 is odd p+7 is even therefore 2| p+7

（b）proof:
we want to proof x^3=27 has a natural number solution,we can find this solution

we have x=3 x^3=3*3*3=27 hence this equation has a natural solution

5(a)disproof:
for any positive ε belong to R,we can choose N>1

such that x=ε/N<ε and -x>ε

(b)disproof:
we can take S={0}⊂N, any t ∈S, t=0, |t|=0<1

追问

太感谢了 我刚回来还没有具体看 如果有不理解的 还希望你能解答

最后一个5（b) 有乱码？

追答

有乱码吗

追问

没事啦 我之前用手机看的 能麻烦在忙我解决下我私聊你的问题嘛 答完 我在给你追加下悬赏

追答

你说来看看

追问

第一张不是 发错了 第二张才是呢

追答

这些题还都是比较简单的吧，你应该多些思考下

proofA: for any x∈R we can take y=x+1 ∈R,such that

(y-x)(y-x-2)=1*（-1）=-1≤0

disproof B: for any y∈R take x=y+1∈R,such that

(y-x)(y-x-2)=(-1)*(-3)=3>0