Question

Let X= (1, 2, 3, 4) and R= {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)) Then R is

(1) Reflexive (2) symmetric (3) transitive (4) equivalence​

Answer 1

Answer:

(1) Reflexive (2) symmetric both

Step-by-step explanation:

Let A={1,2,3,4} and R be a relation on A given by R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3)}.

Now for all 1,2,3,4∈A, (1,1),(2,2),(3,3),(4,4)∈R, this gives the relation R is reflexive.

Again for (1,2)∈R⇒(2,1)∈R and (1,3)∈R⇒(3,1)∈R for 1,2∈A. This gives the relation R is symmetric.

But the relation is not transitive as (2,1),(1,3)∈R but (2,3)



∈R.

Hence the relation is not equivalance.