Jee Main 2024 31 01 2024 Shift1 - Question17

Answer: (13)

Solution:

$R={(1,2),(2,3),(2,4)}$

for reflexive, we need to add the appropriate object pronoun.

$(1,1),(2,2),(3,3),(4,4)$

for symmetric property

if $(1,2) \in R$

then $(2,1) \in R$

if $(2,3) \in R$

then $(3,2) \in R$

if $(2,4) \in R$

then $(4,2) \in R$

So set becomes a set

${(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2), (2,4),(4,2)}$

for transitive verbs

As $(1,2) \in R$

$(2,3) \in R$

then $(1,3) \in R$ and $(3,1) \in R$ (for symmetric)

$\&(1,2) \in R$

$(2,4) \in R$

then $(1,4) \in R$ and $(4,1) \in R$ (for symmetric) $(3,2) \in R$

$(2,4) \in R$

then $(3,4) \in R$ and $(4,3) \in R$ (for symmetric)

so set $S={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2),(2,4),(4,2),(1,3),(3,1),(1,4),(4,1), (3,4),(4,3)}$

so 13 new elements were added

$\Rightarrow n=13$