Consider the relation R = {(x, y) | x, y ∈ Z+ and x + y = 10}. Determine which of the following statements is true.a. R is a Symmetric Relationb. None of the Option is correctc. R is a Transitive Relationd. R is a Antisymmetric Relatione. R is a Reflexive Relation

Given:(1) Let R1 and R2 be two transitive relations on a set A. Then, R1 UNION R2 is a transitive relation on A.(2) Let R be the relation x + y = 0 on the set of all real numbers. Then, R is antisymmetric.Select one of the following choices:Question 10Answera.(1) is True and (2) is Falseb.(1) and (2) are Truec.(1) and (2) are Falsed.(1) is False and (2) is True

rue or false (give reasons):(a) For a symmetric relation R on a nonempty set X, xRy and yRx for each x, y ∈ X(b) For an antisymmetric relation R on a nonempty set X:i. xRy and yRx for each x, y ∈ Xii. R is also a symmetric relation

Let R and S be two non-void relations on a set A. Which of the following statements is false  R and S are transitive Þ R È S is transitive  R and S are transitive Þ R Ç S is transitive  R and S are symmetric Þ R È S is symmetric R and S are reflexive Þ R Ç S is reflexive

etermine whether the each of the relation defined on the set of positive integers is reflexive,symmetric, antisymmetric, or transitive.(a) R = {(x, y) : xy = 2}(b) R = {(x, y) : xy ≥ 1}(c) R = {(x, y) : x = and2}(d) R = {(x, y) : 3 divides (x + 2and)}(It is) R = {(x, y) : x − and = 2}(f) R = {(x, y) : 3 divides (x − an

Which of the properties below does the relationp = {(a,a),(b,c),(c,d),(d,d)}on the set X = {a,b,c,d} have? A It is reflexive. B It is symmetric. C It is transitive. D It is an equivalence relation. E None of the above