# If A = {1, 2, 3,

Given that, A = {1, 2, 3, 4 }

(a) Reflexive, transitive but not symmetric

Let R be a relation defined by

R = {(1,1),(1,2),(1,4),(2,2),(2,3),(3,2),(3,3),(4,2),(4,4)} on set A.

R is reflexive (1,1),(2,2),(3,3),(4,4) R

R is transitive (1,4) R and (4,2) R (1,2) R

R is not symmetric (1,4) R but (4,1) R

Hence, R is reflexive, transitive but not symmetric.

(b) Symmetric but neither reflexive nor transitive

Let R be a relation defined by

R = {(1,2),(2,1),(2,3),(3,2)} on set A.

R is not reflexive (1,1),(2,2),(3,3),(4,4) R

R is symmetric (1,2) R (2,1) R and (2,3) R (3,2) R

R is not transitive (1,2) R and (2,1) R (1,1) R

Hence, R is symmetric but neither reflexive nor transitive.

(c) Reflexive, symmetric and transitive.

Let R be a relation defined by

R = {(1,1),(1,2),(1,4),(2,1),(2,2),(2,3),(3,2),(3,3),(4,1),(4,4)} on set A.

R is reflexive (1,1),(2,2),(3,3),(4,4) R

R is symmetric (1,2),(1,4),(2,3) R (2,1),(4,1),(3,2) R

R is transitive (1,2) R and (2,1) R (1,1) R

Hence, R is reflexive, symmetric and transitive.

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