2 votes 2 votes 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 tifrmaths2015 set-theory&algebra functions + – makhdoom ghaya asked Dec 21, 2015 makhdoom ghaya 508 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes 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 jatinmittal199510 comment Share Follow See 1 comment See all 1 1 comment reply vijaycs commented Dec 1, 2016 reply Follow Share but any logic for other options not being ans ? 0 votes 0 votes Please log in or register to add a comment.