Let R be the relation over the set A of all straight lines in a plane such that $l_1 R ~l_2 \Leftrightarrow l_1$ is parallel to $l_2$. Then R is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → An Equivalence relation
Let P denote → Universal set of planes
for each $l∈P$
$l||l$ so $(l,l)∈R$ (Reflexive)
$(l_1,l_2)∈R$
$⇒l_1||l_2⇒(l_2,l_1)∈R$ (Symmetric)
$(l_1,l_2)∈R,(l_2,l_3)∈R$
$l_1||l_2,l_2||l_3$
$⇒l_1||l_3⇒(l_1,l_3)∈R$ (Transitive)
⇒ Equivalence relation