TIFR-2015-Maths-B-12

makhdoom ghaya asked Dec 21, 2015

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Let $X \subset \mathbb{R}$ and let $f,g : X \rightarrow X$ be a continuous functions such that $f(X)\cap g(X)=\emptyset$ and $f(X)\cup g(X)= X$. Which one of the following sets cannot be equal to $X$?

$[0, 1]$
$(0, 1)$
$[0, 1)$
$\mathbb{R}$

Set Theory & Algebra
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set-theory&algebra
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makhdoom ghaya asked Dec 21, 2015

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I think answer is D since its given that X is a proper subset of R, then how can it be equal to R.

jatinmittal199510 answered Nov 3, 2016

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vijaycs

commented Dec 1, 2016

but any logic for other options not being ans ?

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