Sets, Relations and Function: Let A=\1,2,3,4\ and R:Ato A be the relation defined by… | JEE Main 2013

JEE Main 2013 (Online) 9th AprilQuestion 1

Let $A=\{1,2,3,4\}$ and $R:A\to A$ be the relation defined by $R=\{(1,1),(2,3),(3,4),(4,2)\}$. The correct statement is :

Sets, Relations and Function

$R$ does not have an inverse.$R$ is not a one to one function.$R$ is an onto function.✓ Correct answer$R$ is not a function.

Solution

$R$ assigns $1\mapsto1$, $2\mapsto3$, $3\mapsto4$, $4\mapsto2$: every element has exactly one image and all of $\{1,2,3,4\}$ are images, so $R$ is a bijection, in particular onto.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2013 (Online) 9th April)

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