If A= .1,2,3,4. , then a relation R= .(.1,1.),(.2,2.),(3 , 3),(.4,4.),(.2,4.),(.1,3.),(.1,4.),(.1,2.). on set A is

Question

If A= .1,2,3,4. , then a relation R= .(.1,1.),(.2,2.),(3 , 3),(.4,4.),(.2,4.),(.1,3.),(.1,4.),(.1,2.). on set A is (A) reflexive and symmetric only (B) an equivalence relation (C) reflexive only (D) reflexive and transitive only

Tardigrade Admin · Accepted Answer

∵ (.2,4.)∈ R and (.4,2.)∉ R ∴ not-symmetric and (.1,2.),(.2,4.)∈ R⇒ (.1,4.)∈ R ∴ Transitive ∵ (.a,a.)∈ R∀ a∈ A⇒ reflexive ∴ R is reflexive and transitive.

Q. If $A = {1, 2, 3, 4}$ , then a relation $R = {(1, 1), (2, 2), (3, 3), (4, 4), (2, 4), (1, 3), (1, 4), (1, 2)}$ on set $A$ is

reflexive and symmetric only

an equivalence relation

reflexive only

reflexive and transitive only

$∵ (2, 4) \in R$ and $(4, 2) \in / R$
$∴$ not-symmetric and $(1, 2), (2, 4) \in R \Rightarrow (1, 4) \in R$
$∴$ Transitive
$∵ (a, a) \in R \forall a \in A \Rightarrow$ reflexive
$∴ R$ is reflexive and transitive.

Q. If A={1,2,3,4} , then a relation R={(1,1),(2,2),(3,3),(4,4),(2,4),(1,3),(1,4),(1,2)} on set A is