Which of the following relation is a partial order as well as an equivalence relation?

  1. Home
  2. Back

Question:
Which of the following relation is a partial order as well as an equivalence relation?

1.equal to(=)

2.less than(<)

3. greater than(>)

4.not equal to(!=)

Posted Date:-2022-05-13 09:10:43

More MCQS Questions and answers

  1. Find the interval in which function f(x) = sinx+cosx, 0 ≤ x ≤ 2π is decreasing.
  2. (a,a) ∈ R, for every a ∈ A. This condition is for which of the following relations?
  3. A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) ∊ P. ii)(a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153) The ordered pairs of natural numbers are contained in P are ______ and ______
  4. All closed walks are of ______ length in a bipartite graph.
  5. Bipartite graphs are used in ________
  6. Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________
  7. Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?
  8. Every complete bipartite graph must not be _______
  9. Find the area of a semicircle if the radius is 6 cm.
  10. Find the diameter of the circle if the area of the circle is 6 m.
  11. Find the interval in which function f(x) = sinx+cosx is increasing.
  12. Find the radius of a circle if 2 m is the area of the circle.
  13. Find the radius of the circle if the area of the circle is 22 cm.
  14. Find the radius of the circle if the circumference is 12 m.
  15. Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.
  16. Hasse diagrams are first made by ______
  17. If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______
  18. In a poset (S, ⪯), if there is no element n∈S with m<n, then which of the following is true?
  19. In a poset P({v, x, y, z}, ⊆) which of the following is the greatest element?
  20. In a ______ the degree of each and every vertex is equal.
  21. In which of the following relations every pair of elements is comparable?
  22. Is the function f(x) = 3x+10 is increasing on R?
  23. Let (A, ≤) be a partial order with two minimal elements a, b and a maximum element c. Let P:A –> {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) ⇒ P(b) for all satisfying a ≤ b, where ⇒ stands for logical implication. Which of the following statements cannot be true?
  24. Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______
  25. Let A={1,2,3} and B={4,5,6}. Which one of the following functions is bijective?
  26. Let G be the graph defined as the Hasse diagram for the ⊆ relation on the set S{1, 2,…, 18}. How many edges are there in G?
  27. Let M={5,6,7,8} and N={3,4,9,10}. Which one of the following functions is neither one-one nor onto?
  28. Let P={10,20,30} and Q={5,10,15,20}. Which one of the following functions is one – one and not onto?
  29. Let R be a relation in the set N given by R={(a,b): a+b=5, b>1}. Which of the following will satisfy the given relation?
  30. n undirected graph G which is connected and acyclic is called ____________
  31. The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.
  32. The function f:R→R defined as f(x)=7x+4 is both one-one and onto.
  33. The inclusion of ______ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.
  34. The less-than relation, <, on a set of real numbers is ______
  35. The maximum number of edges in a bipartite graph on 14 vertices is ___________
  36. The relation ≤ is a partial order if it is ___________
  37. The spectrum of a graph is _______ if and only if it is _______ graph.
  38. What is the circumference of a circle if the radius is 7 m?
  39. What is the circumference of the circle if the radius is 121 cm?
  40. What is the maximum number of edges in a bipartite graph on 14 vertices?
  41. What is the nature of function f(x) = 7x-4 on R?
  42. Which graph represents relation between whole and its parts?
  43. Which of the following relation is a partial order as well as an equivalence relation?
  44. Which of the following relations is reflexive but not transitive for the set T = {7, 8, 9}?
  45. Which of the following relations is symmetric and transitive but not reflexive for the set I = {4, 5}?
  46. Which of the following relations is symmetric but neither reflexive nor transitive for a set A = {1, 2, 3}.
  47. Which of the following relations is transitive but not reflexive for the set S={3, 4, 6}?
  48. Which of these is not a type of relation?
Search
R4R Team
R4Rin Top Tutorials are Core Java,Hibernate ,Spring,Sturts.The content on R4R.in website is done by expert team not only with the help of books but along with the strong professional knowledge in all context like coding,designing, marketing,etc!