Daniel J Smith Custom TMUA alpha · Question 16

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Daniel J Smith Custom TMUA alpha · Q16

Logic & proof

Consider the following statement about irrational numbers:

$(*)$ If $x$ and $y$ are irrational numbers, then $x+y$ is irrational.

Which of the following pair(s) $(x,y)$ provide(s) a counterexample to $(*)$ ?

I: $x=\sqrt2$ , $y=\sqrt2$

II: $x=\sqrt2$ , $y=3$

III: $x=1+\sqrt2$ , $y=1-\sqrt2$

Anone of them

BI only

CII only

DIII only

EI and II only

FI and III only

GII and III only

HI, II and III

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