In each case below, a relation on the set {1, 2, 3} is given. of the three properties, reflexivity, symmetry, and transitivity, determine which ones the relation has. give reasons.

a. is symmetric but not reflexive and transitive

b. is reflexive and transitive but not symmetric

c. is reflexive, symmetric and transitive

Step-by-step explanation:

The cases are missing in the question.

Let the cases be as follows:

a. R = {(1, 3), (3, 1), (2, 2)}

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)}

c. R = ∅

R is defined on the set {1, 2, 3}

a.  R = {(1, 3), (3, 1), (2, 2)} is

b. R = {(1, 1), (2, 2), (3, 3), (1, 2)} is

is reflexive because (1, 1), (2, 2), (3, 3) is in R

is not symmetric because for (1,2) (2,1) is not in R

is transitive becaue for (1,1) and (1,2) we have (1,2) in R

c. R = ∅ is

reflexive, symmetric and transitive because it satisfies the definitions since there is no counter example.

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.