Question 1042855
.
Let a, b ∈ R. Prove using contradiction that if a ∈ Q and ab ∉ Q then b ∉ Q.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let assume that b &#8712; Q.   (1)

Then  ab &#8712; Q.

But  ab &#8713; Q, according to the condition.

Contradiction.

It means that the original assumption (1) is wrong.

Hence,  b &#8713; Q.

QED.
</pre>

Proved.


_______________
(*)  Actually, it is usually considered as trivial and obvious statement . . .