Let L be the set of all lines in a plane and R be the relation in L, defined as R={$(L_1,L_2):L_1$ is perpendicular to $L_2$ } then R is :
A . Reflexive
B. Symmetric
C. Neither reflexive nor transitive
D. Transitive
E. Neither reflexive nor symmetric
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → B, C only
R is not reflexive
as no line is perpendicular to itself
R is symmetric
as if $(L_1,L_2)∈R⇒L_1⊥L_2⇒(L_2,L_1)∈R$
R is not transitive
as $(L_1,L_2)∈R,(L_2,L_3)∈R⇒L_1⊥L_2$ and $L_2⊥L_3 ⇒ L_1||L_3$
so B, C are only correct