Determine whether the relation R in the set A = {1, 2, 3, ……… 13

1.	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 arid transitive.
Answer» y = 3x R – {(1,3) (2,6) (3, 9) (4,12)} R is not reflexive as (1, 1) ∉ R R is not symmetric as (1,3) ∈ R but (3,1) ∉ R R is not transitive as (1,3) ∈ R, (3,9) ∈ R but (1,9)∉ R

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 arid transitive.

Answer»

y = 3x

R – {(1,3) (2,6) (3, 9) (4,12)}

R is not reflexive as (1, 1) ∉ R

R is not symmetric as (1,3) ∈ R but

(3,1) ∉ R R is not transitive as

(1,3) ∈ R, (3,9) ∈ R but (1,9)∉ R

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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 arid transitive.

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