Suppose that the following relations are defined on the set A = {1, 2, 3, 4}.R1={(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)},
R2={(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)},
R3={(2,4),(4,2)} ,
R4={(1,2),(2,3),(3,4)},
R5={(1,1),(2,2),(3,3),(4,4)},
R6={(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)},

Determine which of these statements are correct.
Type ALL correct answers below.

A. R1 is not symmetric

B. R3 is symmetric

C. R3 is transitive

D. R2 is reflexive

E. R4 is symmetric

F. R1 is reflexive

G. R5 is not reflexive

H. R5 is transitive

I. R3 is reflexive

J. R2 is not transitive

K. R4 is transitive

L. R4 is antisymmetric

M. R6 is symmetric

A relation R over set A is symmetric if for all x, y from A the following is true: (x,y) is in R implies (y,x) is in R. Definition 2: A relation R over set A is symmetric if for all x, y from A the following is true: if (x,y) is in R, then (y,x) is in R.

a set A is called transitive if either of the following equivalent conditions hold: whenever x ∈ A, and y ∈ x, then y ∈ A. whenever x ∈ A, and x is not an element, then x is a subset of A.

Reflexive relation on set is a binary element in which every element is related to itself. Let A be a set and R be the relation defined in it. R is set to be reflexive, if (a, a) ∈ R for all a ∈ A that is, every element of A is R-related to itself.

A relation R on a set A is called antisymmetric if and only if for any a, and b in A, whenever <a, b> R , and <b, a> R , a = b must hold. Equivalently, R is antisymmetric if and only if whenever <a, b> R , and a b , <b, a> R .

lhmarianateixeira lhmarianateixeira · Answer 2 · 2021-12-19T14:24:21+01:00

in this exercise we have to use the knowledge of the relations of the R sets, in this way to classify whether the alternatives are correct or incorrect:

A) Incorrect

B) Correct

C) Correct

D) Incorrect

E) Incorrect

F) Incorrect

G) Incorrect

H) Correct

I) Correct

J) Incorrect

K) Incorrect

L) Correct

M) Correct

To classify each of the alternatives we need to identify what each one means, thus:

Symmetric: A relation R over sets A is symmetric if for all x, y from A the following is true: (x,y) is in R implies (y,x) is in R. Definition 2: A relation R over sets A is symmetric if for all x, y from A the following is true: if (x,y) is in R, then (y,x) is in R.

Not symmetric: A relation R on a sets A is called antisymmetric if and only if for any a, and b in A, whenever <a, b> R , and <b, a> R , a = b must hold. Equivalently, R is antisymmetric if and only if whenever <a, b> R , and a b , <b, a> R .

Transitive: a set A is called transitive if either of the following equivalent conditions hold: whenever x ∈ A, and y ∈ x, then y ∈ A. whenever x ∈ A, and x is not an element, then x is a subset of A.

Reflexive: relation on sets is a binary element in which every element is related to itself. Let A be a set and R be the relation defined in it. R is set to be reflexive, if (a, a) ∈ R for all a ∈ A that is, every element of A is R-related to itself.

See more about sets at brainly.com/question/8053622