Question

Let R = {(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)} be a relation on the set A = {3, 5, 9, 12}. Then, R is:(a) reflexive, symmetric but not transitive.(b) symmetric, transitive but not reflexive.(c) an equivalence relation.(d) reflexive, transitive but not symmetric.

Answer 1

Let R = {(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)} be a relation on the set A = {3, 5, 9, 12}. Then, R is:(a) reflexive, symmetric but not transitive.(b) symmetric, transitive but not reflexive.(c) an equivalence relation.(d) reflexive, transitive but not symmetric.

Answer 2

∴R is symmetric ,transitive but not symmetric.

Step-by-step explanation:

Given R = {(3,3),(5,5),(9,9),(12,12),(5,12),(3,9),(3,12),(3,5)}

and A={3,5,9,12}

Reflexive

a∈A  then  (a,a)∈R

since (3,3),(5,5),(9,9)and (12,12)∈R

so R is reflexive.

symmetric

If a and b∈ A and (a,b)∈R then (b,a) ∈R

Here (5,12)∈R but (12,5)∉R

so R is not symmetric.

Transitive

If a,b and c ∈ A and (a,b) and(b,c)∈R

Then (a,c)∈R

Here (5,5) and (5,12) ∈R ⇒(5,12)∈R

So R is transitive.