Consider the binary relation R = {(x,y),(x,z),(z,x),(z,y)} on the set (x,y,z}, which one of the following is true? " O Ris symmetric but Not antisymmetric O Ris both symmetric and antisymmetric O Ris not symmetric but antisymmetric O Ris neither symmetric nor antisymmetric

Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric, antisymmetric, or transitive.

Please just answer parts iv. and v.

Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

Show that the relation R on ZxZ defined by (a, b) R (c, d) if and only if a + d = b + c is an equivalence relation.

For each of the relations on A = {0, 1, 2, 3} belowR = {(0, 0),(0, 1),(0, 3),(1, 0),(1, 1),(2, 2),(3, 0),(3, 3)},S = {(0, 0),(0, 2),(0, 3),(2, 3)},T = {(0, 1),(2, 3)}determine whether they are reflexive, symmetric or transitive. List all that apply andjustify your answers.

100}) by if and only if |An B is even. Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Justify your ans Let R be the relation defined on P({1,.. ARB

3 For the equivalence relation on {0, 1,2,3,4} defined as {(x, y) : x +y is even} (a) Write it out as a list of ordered pairs (b) List the cells in the associated partition.

For the binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, which of the following statements would be true? R={ (0,4), (1, 1), (1, 3), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4) } where A = {0, 1,2, 3, 4} Select one: O Ris symmetric but not antisymmetric O Ris antisymmetric but not symmetric O Ris both symmetric and antisymmetric O none of these options O Ris neither symmetric nor antisymmetric

Let A = {1, 3, 7, 9} and S be the binary relation on A definedby: x S y <=>x^3 ≡ y (mod 10)(a) State explicitly which ordered pairs are in S.(b) State explicitly which ordered pairs are in S^-1.(c) Is S reflexive? Yes or No? (circle one, no proofs.)(d) Is S symmetric? Yes or No? (circle one, no proofs.)(e) Is S transitive? Yes or No? (circle one, no proofs.)