Varss
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Hi I am preparing for the ECAA exam and I came across this question in a past paper and I don't see why the correct answer is A, not C. Any help is appreciated.
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Varss
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RDKGames
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(Original post by Varss)
....
Statement (2) fails. It claims that \dfrac{x}{y} > 1 \iff \dfrac{y}{x} < 1.

However, this is the same as saying:

(A) \dfrac{x}{y} > 1 \implies \dfrac{y}{x} < 1

*and*

(B) \dfrac{x}{y} > 1 \Longleftarrow \dfrac{y}{x} < 1


Part (B) of this statement fails. For instance, pick y=-1 and x=1 then the second inequality is satisfied, but the first one isn't.
Last edited by RDKGames; 3 months ago
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Physics Enemy
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(Original post by Varss)
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x = -2, y = -1 disproves 1) (-2/-1 > 1 but -2 < -1)
y = -2, x = 1 disproves 2) (-2/1 < 1 but 1/-2 < 1)
x = 2, y = 1/4 disproves 3) (2*1/4 < 1 yet x > 1)
Last edited by Physics Enemy; 3 months ago
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Varss
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(Original post by RDKGames)
Statement (2) fails. It claims that \dfrac{x}{y} &gt; 1 \iff \dfrac{y}{x} &lt; 1.

However, this is the same as saying:

(A) \dfrac{x}{y} &gt; 1 \implies \dfrac{y}{x} &lt; 1

*and*

(B) \dfrac{x}{y} &gt; 1 \Longleftarrow \dfrac{y}{x} &lt; 1


Part (B) of this statement fails. For instance, pick y=-1 and x=1 then the second inequality is satisfied, but the first one isn't.
Oh I see, I didn't understand the logic statement properly. Thank you.
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