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

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

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

Let A = {1, {1}, 3, 4, {5, 6}} be a set, and let B and C be the following relations on A:            B = {(1, 3), (4, 1), (3, {5, 6}), ({1}, 4), ({5, 6}, {1})}            C = {(1, 1), (3, 4), (4, 3), ({5, 6}, {1})The relation B is antisymmetric.a.Trueb.False

Let R be the relation on Z≥ (the set of integers) defined by (x, y) ∈ R iff x2 + y2 = 2k for some integers k ≥0.R is not antisymmetric.Which of the following ordered pairs can be used together in a counterexample to prove that R is not antisymmetric? (Remember that R is defined on Z≥)a.(–1, 1) and (1, –1)b.(5, 9) and (13, 15)c.(8, 7) and (7, 8)d.(3, 1) and (1, 3)

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