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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $A = {-2, -1, 0, 1, 2, 3, 4}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x + y \le 2$. Let $\ell$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations respectively. Then $\ell + m + n$ is equal to:
Solution
$R = {(-2,a), (-1,b), (0,c), (1,d), (2,e)}$
$a = {-2,-1,0,1,2,3,4}$
$b = {-2,-1,0,1,2,3,4}$
$c = {-2,-1,0,1,2}$
$d = {-2,-1,0}$
$e = {-2}$
$\therefore$ No. of elements in $R = 7 + 7 + 5 + 3 + 1 = 23 = \ell$
Minimum number of elements to be added to make it reflexive
$m = 4 \Rightarrow (1,1), (2,2), (3,3), (4,4)$
Minimum number of elements to be added to make it symmetric
$n = 6$
$\therefore \ell + m + n = 23 + 4 + 6 = 33$
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