6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive, and if all elements of X are comparable (that is, for every pair x₁, x2 € X either x₁ Rx2 or x2 Rx1). (a) Construct a total order on the set X = {a, B, Ⓒ, 13}. (b) How many possible total orders are there on a finite set of cardinality n?

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

A:

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

A:

Q: The relation D is defined on the set P = {6, 9, 15, 54, 78, 90} by the rule: n1 D n2 exactly if (n2…

A: (i) The relation D is defined on the set P=6, 9, 15, 54, 78, 90 by the following rule: n1 D n2…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

Q: Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1),…

A:

Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

A:

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

A:

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

A:

Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

A:

Q: (a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence…

A:

Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…