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2.Relations and Functions
easy
$A=\{1,2,3, \ldots, 14\} .$ $R = \{ (x,y):3x - y = 0,$ જ્યાં $x,y \in A\} .$ જો એ $A$ થી $A$ નો સંબંધ હોય, તો $R$ નો પ્રદેશ, સહપ્રદેશ અને વિસ્તાર મેળવો.
Option A
Option B
Option C
Option D
Solution
The relation $R$ from $A$ to $A$ is given as $R = \{ (x,y):3x – y = 0,{\rm{ }}$ where $x,y \in A\} $
ie., $R=\{(x, y): 3 x=y, $ where $ x, y \in A\}$
$\therefore R=\{(1,3),(2,6),(3,9),(4,12)\}$
The domain of $R$ is the set of all first elements of the ordered pairs in the relation.
$\therefore$ Domain of $R=\{1,2,3,4\}$
The whole set $A$ is he codomain of the relation $R$.
$\therefore$ Codomain of $R=A=\{1,2,3 \ldots .14\}$
The range of $R$ is the set of all second elements of the ordered pairs in the relation.
$\therefore$ Range of $R=\{3,6,9,12\}$
Standard 11
Mathematics
