Let A = {1, 2, 3} and R= {(1, 3), (3, 3)]. Findwhether the relation is

1.	Let A = {1, 2, 3} and R= {(1, 3), (3, 3)]. Findwhether the relation is (i) reflexive (ii) symmetrie(iii) transitive.The answer is only transitive.Answer it if you know the answer.How is it transitive?
Answer» DETERMINE WHETHER the RELATION R in the set A={1,2,3,.. 13,14} defined as R={(x,y):3x−y=0}, is REFLEXIVE, symmetric and transitive. Answer Relation R on the set A={1,2,3,.,13,14} is defined as R={(x,y):3x−y=0} Let a∈A R is reflexive if (a,a)∈R if 3a−a=0 if 3a=a i.e. if 3=1 which is not true Thus, R is not reflexive (1) Let a,b∈A such that (a,b)∈R ⟹3a−b=0 ⟹3a=b This does not imply 3b=a i.e 3b−a=0 ∴(b,a) does not BELONG to R ∴ For a,b∈A, (a,b)∈R⟹(b,a) is not in R. Thus, R is not symmetric. . (2) Let a,b,c∈A such that (a,b),(b,c)∈R ⟹3a−b=0,3b−c=0 ⟹3a=b,3b=c ⟹3a= 3 c ⟹9a=c This does not imply (a,c)∈R ∴ For a,b,c∈A, (a,b),(b,c)∈R does not imply (a,c)∈R Hence, R is non-reflexive, non-symmetric and non-transitive. Please brainlest me the answer

Let A = {1, 2, 3} and R= {(1, 3), (3, 3)]. Findwhether the relation is (i) reflexive (ii) symmetrie(iii) transitive.The answer is only transitive.Answer it if you know the answer.How is it transitive?

Answer»

DETERMINE WHETHER the RELATION R in the set A={1,2,3,.. 13,14} defined as R={(x,y):3x−y=0}, is REFLEXIVE, symmetric and transitive.

Answer

Relation R on the set A={1,2,3,.,13,14} is defined as R={(x,y):3x−y=0}

Let a∈A

R is reflexive if (a,a)∈R

if 3a−a=0

if 3a=a i.e. if 3=1 which is not true

Thus, R is not reflexive (1)

Let a,b∈A such that (a,b)∈R

⟹3a−b=0

⟹3a=b

This does not imply 3b=a i.e 3b−a=0

∴(b,a) does not BELONG to R

∴ For a,b∈A, (a,b)∈R⟹(b,a) is not in R.

Thus, R is not symmetric. . (2)

Let a,b,c∈A such that (a,b),(b,c)∈R

⟹3a−b=0,3b−c=0

⟹3a=b,3b=c

⟹3a=

⟹9a=c

This does not imply (a,c)∈R

∴ For a,b,c∈A, (a,b),(b,c)∈R does not imply (a,c)∈R

Hence, R is non-reflexive, non-symmetric and non-transitive.

Please brainlest me the answer