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)

[匿名]

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.

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