For each true statement below, give a proof. For each false statement below, write out its negation and prove?

2012-02-03 3:01 am
For each true statement below, give a proof. For each false statement below, write out
its negation and prove that. In parts (e) and (f), use only the definitions of rational and
irrational
http://img854.imageshack.us/img854/2338/47618948.jpg
you don't have to answer all, just one or 2 is fine
please help me , plz ty!!!!!!!!

回答 (1)

2012-02-03 4:53 am
✔ 最佳答案
e. a irrational, a+b rational ==> b is irrational.
True
Assume b is rational. Then a = (a+b) + (-b) = the sum of two rationals, which must be rational.
But a is irrational, so we have a contradiction. Therefore b mus be irrational.

f. True, but for a strange reason: the premise is false. In logic, A false statement can imply anything. The premise is false by (e) above and the fact that 1 is rational.
Since we've proved the premise is false, we've proved the statement is true.
QED

For the others, maybe you should define the symbols for us.


收錄日期: 2021-05-01 00:54:37
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120202190145AAQQoVd

檢視 Wayback Machine 備份