Question

Let $x\in Q,y\in Q^c$, which of the following statement is always WRONG ?

• A. $xy\in Q^c$
• B. $y/x\in Q$, whenever defined
• C. $\sqrt{2}x+y\in Q$
• D. $x/y\in Q^c$, whenever defined

Answer 1

Answer: (B)

$y/x\in Q$, whenever defined

Let $x=1,y=\sqrt{2}$
Then $xy=\sqrt{2}\in Q^c$
Obvious
$x=-1,y=\sqrt{2}$ then $\sqrt{2}x+y=0\in Q$
$x=1,y=\sqrt{2}$ then $x/y=\frac{1}{\sqrt{2}}\in Q^c$