McqMate
Chapters
| 1. |
Define f(n) = n/2 + 1−(−1)n/4 for all n 2 Z. Thus, f: Z → Z, Z the set of all integers.Which is correct? |
| A. | f is a function and is onto but not one-to-one. |
| B. | f is a function and is onto and one-to- one. |
| C. | f is a function and is not onto but is one-to-one. |
| D. | f is a function and is not onto and not one-to-one |
| Answer» A. f is a function and is onto but not one-to-one. | |
| 2. |
If f (x) = cos x and g(x) = x3 , then (f o g) (x) is |
| A. | (cos x)3 |
| B. | cos 3 x |
| C. | X (cos x )3 |
| D. | cos x3 |
| Answer» D. cos x3 | |
| 3. |
Transitivity and irreflexive imply: |
| A. | Symmetric |
| B. | Reflexive |
| C. | Irreflexive |
| D. | Asymmetric |
| Answer» D. Asymmetric | |
| 4. |
If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is |
| A. | {(3,3), (3,4), (3,5)} |
| B. | {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)} |
| C. | {(3,3), (3,5), (5,3), (5,5)} |
| D. | {(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)} |
| Answer» C. {(3,3), (3,5), (5,3), (5,5)} | |
| 5. |
A relation that is reflexive, anti-symmetric and transitive is a |
| A. | Function |
| B. | equivalence relation |
| C. | partial order |
| D. | None of these |
| Answer» C. partial order | |
| 6. |
Let f : X →Y and g : Y → Z. Let h = go f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE? |
| A. | If f is one-to-one then h is one-to- one and onto. |
| B. | If f is not onto then h is not onto. |
| C. | If f is not one-to- one then h is not one-to-one. |
| D. | If f is one-to-one then h is one-to- one. |
| Answer» A. If f is one-to-one then h is one-to- one and onto. | |
| 7. |
Domain and Range of the function Y = –v(–2x + 3) is |
| A. | x=3/2, y=0 |
| B. | x>3/2, y=0 |
| C. | x<3/2, y=0 |
| D. | x=3/2, y=0 |
| Answer» D. x=3/2, y=0 | |
| 8. |
The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is |
| A. | Reflexive |
| B. | Transitive |
| C. | Symmetric |
| D. | Asymmetric |
| Answer» B. Transitive | |
| 9. |
A partial ordered relation is transitive, reflexive and |
| A. | Anti-symmetric |
| B. | Bisymmetric |
| C. | Anti-reflexive. |
| D. | Asymmetric |
| Answer» A. Anti-symmetric | |
| 10. |
Find the number of relations from A = {cat, dog, rat} to B = {male , female} |
| A. | 64 |
| B. | 6 |
| C. | 32 |
| D. | 15 |
| Answer» A. 64 | |
| 11. |
The number of distinct relations on a set of 3 elements is |
| A. | 8 |
| B. | 9 |
| C. | 18 |
| D. | 512 |
| Answer» C. 18 | |
| 12. |
How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set? |
| A. | 2n |
| B. | 2n - 1 |
| C. | 2n - 2 |
| D. | 2(2n – 2) |
| Answer» C. 2n - 2 | |
| 13. |
How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric? |
| A. | 2n(n+1)/2 and 2n.3n(n–1)/2 |
| B. | 3n(n–1)/2 and 2n(n–1) |
| C. | 2n(n+1)/2 and 3n(n–1)/2 |
| D. | 2n(n+1)/2 and 2n(n–1)/2 |
| Answer» D. 2n(n+1)/2 and 2n(n–1)/2 | |
| 14. |
The number of functions from an m element set to an n element set is: |
| A. | mn |
| B. | m+n |
| C. | nm |
| D. | m*n |
| Answer» A. mn | |
| 15. |
Let R = {(a, a), (a, b)} be a relation on S = {a, b, c}. Then R is not reflexive and not symmetric. |
| A. | T |
| B. | F |
| Answer» A. T | |
| 16. |
Let R = {(a, a), (a, b)} be a relation on S = {a, b, c}. Then R is not transitive. |
| A. | T |
| B. | F |
| Answer» B. F | |
| 17. |
The function f : Z → Z given by f (x)= x +1 is a bijection. |
| A. | T |
| B. | F |
| Answer» A. T | |
| 18. |
The function f : A → B is injective if whenever f (x)= f (y), where x, y € A, then x = y. |
| A. | T |
| B. | F |
| Answer» A. T | |
| 19. |
Let A be a finite set. If f : A → A is injective then it is surjective. |
| A. | T |
| B. | F |
| Answer» A. T | |
| 20. |
The union of two equivalence relations on a non- empty set is an equivalence relation. |
| A. | T |
| B. | F |
| Answer» B. F | |
| 21. |
If A is a set with 3 elements, how many equivalence relations are there on A? Hint: The set of equivalence classes for a given equivalence relation on A is a partition of the set A. |
| A. | 4 |
| B. | 5 |
| C. | 23 |
| D. | 29 |
| Answer» B. 5 | |
| 22. |
Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f =
|
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 23. |
A relation R is defined on Z by xRy if 2x +5y = 0(mod7). Then the equivalence class[10] is equal to the equivalence class… |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» A. 3 | |
| 24. |
Let R be a relation on a set A = {1, 2, 3, 4} given by R =
|
| A. | reflexive and symmetric, but not transitive. |
| B. | reflexive and transitive, but not symmetric. |
| C. | symmetric and transitive, but not reflexive. |
| D. | reflexive, but neither symmetric nor transitive. |
| Answer» C. symmetric and transitive, but not reflexive. | |
| 25. |
If f (x) = -3x - 5, what is the value of f (2)? |
| A. | -11 |
| B. | -1 |
| C. | 1 |
| D. | 11 |
| Answer» A. -11 | |
| 26. |
If g (x) = 3x² - 2x - 5, what is the value of g (-1)? |
| A. | -4 |
| B. | -10 |
| C. | 6 |
| D. | 0 |
| Answer» A. -4 | |
| 27. |
Which relation is not a function? |
| A. | {(2,5), (3,6), (4,7), (5,8)} |
| B. | {(6,-2), (-4,6), (- 2,4), (1,0)} |
| C. | {(-1, 5), (-2,5), (- 3,5), (-4,5)} |
| D. | {(0,-2), (1,0), (-1,- 3), (0,-1)} |
| Answer» D. {(0,-2), (1,0), (-1,- 3), (0,-1)} | |
| 28. |
Consider the recurrence relation ak = -8ak-1 - 15ak-2 with initial conditions a0 = 0 and a1 = 2. Which of the following is an explicit solution to this recurrence relation? |
| A. | ak = (-3)k - (-5)k |
| B. | ak = k(-3)k - k(- 5)k |
| C. | ak = k(-3)k - (-5)k |
| D. | ak = (-5)k - (-3)k |
| Answer» A. ak = (-3)k - (-5)k | |
| 29. |
Consider the recurrence relation ak = 6ak-1 - 9ak-2 with initial conditions a0 = 0 and a1 = 2. Which of the following is an explicit solution to this recurrence relation, provided the constants A and B are chosen correctly? |
| A. | an = A3n + B3n |
| B. | an = A3n + B(-3)n |
| C. | an = A3n + nB3n |
| D. | an = A(-3)n + nB(- 3)n |
| Answer» C. an = A3n + nB3n | |
| 30. |
The binary relation R = {(0, 0), (1, 1)} on A = {0, 1, 2, 3, } is |
| A. | Reflexive, Not Symmetric, Transitive |
| B. | Not Reflexive, Symmetric, Transitive |
| C. | Reflexive, Symmetric, Not Transitive |
| D. | Reflexive, Not Symmetric, Not Transitive |
| Answer» B. Not Reflexive, Symmetric, Transitive | |
| 31. |
Define a binary relation R = {(0, 1), (1, 2), (2, 3), (3, 2), (2, 0)} on A = {0, 1, 2, 3}. The directed graph (including loops) of the transitive closure of this relation has |
| A. | 16 arrows |
| B. | 12 arrows |
| C. | 8 arrows |
| D. | 6 arrows |
| Answer» A. 16 arrows | |
| 32. |
Let N+ denote the nonzero natural numbers. Define a binary relation R on N+ × N+ by (m, n)R(s, t) if gcd(m, n) = gcd(s, t). The binary relation R is |
| A. | Reflexive, Not Symmetric, Transitive |
| B. | Not Reflexive, Symmetric, Transitive |
| C. | Reflexive, Symmetric, Not Transitive |
| D. | Reflexive, Not Symmetric, Not Transitive |
| Answer» A. Reflexive, Not Symmetric, Transitive | |
| 33. |
Define a binary relation R on a set A to be anti- reflexive if xRx doesn’t hold for any x 2 A. The number of symmetric, anti-reflexive binary relations on a set of ten elements is |
| A. | 210 |
| B. | 250 |
| C. | 245 |
| D. | 290 |
| Answer» C. 245 | |
| 34. |
Define an equivalence relation R on the positive integers A = {2, 3, 4, . . . , 20} by m R n if the largest prime divisor of m is the same as the largest prime divisor of n. The number of equivalence classes of R is |
| A. | 8 |
| B. | 10 |
| C. | 9 |
| D. | 11 |
| Answer» A. 8 | |
| 35. |
Consider the divides relation, m | n, on the set A = {2, 3, 4, 5, 6, 7, 8, 9, 10}. The cardinality of the covering relation for this partial order relation (i.e., the number of edges in the Hasse diagram) is |
| A. | 6 |
| B. | 5 |
| C. | 8 |
| D. | 7 |
| Answer» D. 7 | |
| 36. |
Let A = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} and consider the divides relation on A. Let C denote the length of the maximal chain, M the number of maximal elements, and m the number of minimal elements. Which is true? |
| A. | C = 3, M = 8, m = 6 |
| B. | C = 4, M = 8, m = 6 |
| C. | C = 3, M = 6, m = 6 |
| D. | C = 4, M = 6, m = 4 |
| Answer» A. C = 3, M = 8, m = 6 | |
| 37. |
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? |
| A. | R is symmetric but NOT antisymmetric |
| B. | R is NOT symmetric but antisymmetric |
| C. | R is both symmetric and antisymmetric |
| D. | R is neither symmetric nor antisymmetric |
| Answer» D. R is neither symmetric nor antisymmetric | |
| 38. |
Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are: |
| A. | n and n |
| B. | 2 n and n |
| C. | 2 n and 0 |
| D. | n and 1 |
| Answer» A. n and n | |
| 39. |
Which one of the following is the example of nonlinear data structure? |
| A. | Graph |
| B. | Binary Tree |
| C. | Queue |
| D. | Link List |
| Answer» A. Graph | |
| 40. |
If |A|=5 and |B|=4, then there exists an injective function f: B→A. |
| A. | T |
| B. | F |
| Answer» B. F | |
| 41. |
The set of even integers is well-ordered. |
| A. | T |
| B. | F |
| Answer» B. F | |
| 42. |
If n is an integer and x is an irrational real number, then nx is irrational. |
| A. | T |
| B. | F |
| Answer» B. F | |
| 43. |
In Z7, if [6]x =[3]then x =? . |
| A. | [1] |
| B. | [2] |
| C. | [3] |
| D. | [4] |
| Answer» D. [4] | |
| 44. |
Which statement represents "all numbers between negative 4 and positive 8" ? |
| A. | -4 > x > 8 |
| B. | -4 < x < 8 |
| C. | -4 > x < 8 |
| D. | None of these |
| Answer» B. -4 < x < 8 | |
| 45. |
Which interval notation represents the set of numbers that are greater than or equal to -1, but are less than 9? |
| A. | (-1,9] |
| B. | [-1,9] |
| C. | (-1,9) |
| D. | [-1,9) |
| Answer» D. [-1,9) | |
| 46. |
Given the relation D = {(6,4), (8,-1), (x,7), (-3,-6)}. Which of the following values for x will make relation D a function? |
| A. | -3 |
| B. | -6 |
| C. | 8 |
| D. | 6 |
| Answer» A. -3 | |
| 47. |
Which statement is true about the relation shown at the right? |
| A. | It is a function because there exists one y- coordinate for each x- coordinate. |
| B. | It is a function because there exists one x- coordinate for each y-coordinate. |
| C. | It is not a function because there are multiple x-values for a given y-value. |
| D. | It is not a function because there are multiple y-values for a given x- value. |
| Answer» C. It is not a function because there are multiple x-values for a given y-value. | |
| 48. |
A ball is tossed in the air in such a way that the path of the ball is modeled by the equation y = -x² + 6x, where y represents the height of the ball in feet and x is the time in seconds. At what time, x, is the ball at its highest point? |
| A. | 6 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 49. |
Let S = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}. What is the
|
| A. | 10 |
| B. | 7 |
| C. | 9 |
| D. | 8 |
| Answer» D. 8 | |
| 50. |
If S is a set containing n elements then number of elements in power set of S ,i.e.P(S) |
| A. | n |
| B. | 2n |
| C. | 2n |
| D. | n2 |
| Answer» C. 2n | |
| 51. |
If A and B are two non empty sets then cartesian product of A and B is---------- |
| A. | AΧB={(a,b);a,bϵA } |
| B. | AΧB={(a,b);a,bϵB} |
| C. | AΧB={(a,b);aϵA and bϵB} |
| D. | AΧB={(a,b);aϵB and bϵA} |
| Answer» C. AΧB={(a,b);aϵA and bϵB} | |
| 52. |
If set A contains n elements, set B contains m elements then number of elements in AXB is--- |
| A. | m+n |
| B. | n-m |
| C. | m.n |
| D. | n/m |
| Answer» C. m.n | |
| 53. |
If A,B and C are non empty sets then AX(B∩C) is-----. |
| A. | (AXB)U(AXC) |
| B. | (AXB)∩(AXC) |
| C. | (AXB)∩C |
| D. | (AXC)∩B |
| Answer» B. (AXB)∩(AXC) | |
| 54. |
If A,B and C are non empty sets then AX(BUC) is-----. |
| A. | (AXB)U(AXC) |
| B. | (AXB)∩(AXC) |
| C. | (AXB)UC |
| D. | (AXC)UB |
| Answer» A. (AXB)U(AXC) | |
| 55. |
If R is a relation defined from set A to set B then------ |
| A. | R=AXB |
| B. | RCAXB |
| C. | RCBXA |
| D. | AXBCR |
| Answer» B. RCAXB | |
| 56. |
If A=(1,2,3} and R on A is defined by R={(1,1),(2,2),(3,3)} then R is………… |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | All of these |
| Answer» A. Reflexive | |
| 57. |
If A=(1,2,3} and R on A is defined by R={(1,2),(2,1),(1,1),(2,2)} then R is………… |
| A. | Reflexive and symmetric |
| B. | Reflexive and Transitive |
| C. | Symmetric and Transitive |
| D. | All of the above. |
| Answer» C. Symmetric and Transitive | |
| 58. |
Which statement is true? |
| A. | Relation can be of the type one many |
| B. | Function can be of the type one many |
| C. | Both (a) and (b) |
| D. | None of these. |
| Answer» B. Function can be of the type one many | |
| 59. |
Which statement is true? |
| A. | Every function is a relation. |
| B. | Every Relation is a function. |
| C. | Both A and B. |
| D. | None of these. |
| Answer» A. Every function is a relation. | |
| 60. |
In-----Relation every element is related with itself. |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | None |
| Answer» A. Reflexive | |
| 61. |
The Relation is----------if a has relation with b and b has relation with a. |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | None |
| Answer» B. Symmetric | |
| 62. |
If a has relation with b and b has relation with c then a has relation with c is………………..Relation. |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | None |
| Answer» C. Transitive | |
| 63. |
Types of function Mappings are----- |
| A. | One to one |
| B. | Many to one |
| C. | Into, Onto |
| D. | All |
| Answer» D. All | |
| 64. |
The Transitive Closure of a relation R is denoted by---- |
| A. | R* |
| B. | R |
| C. | R+ |
| D. | RR |
| Answer» A. R* | |
| 65. |
The alternative method to find transitive closure of R* is-------. |
| A. | R* |
| B. | RR |
| C. | Warshall’s Algorithm |
| D. | R |
| Answer» C. Warshall’s Algorithm | |
| 66. |
Poset is a------ |
| A. | Positive set |
| B. | p-set |
| C. | P* |
| D. | Partially Ordered set |
| Answer» D. Partially Ordered set | |
| 67. |
If A is any non-empty set and R is a partial ordered relation on set A, then the ordered pair (A,R) is called ------- |
| A. | Poset |
| B. | p-set |
| C. | Positive set |
| D. | None |
| Answer» A. Poset | |
| 68. |
Let (A, ≤) be a poset. A subset of A is known as ------if every pair of elements in the subset are related. |
| A. | Chain |
| B. | Antichains |
| C. | Group |
| D. | Lattice. |
| Answer» A. Chain | |
| 69. |
The number of elements in the chain is called as------ |
| A. | Chain |
| B. | Antichains |
| C. | None |
| D. | Length of chain |
| Answer» D. Length of chain | |
| 70. |
A ------ is a poset (A, ≤) in which every subset {a, b} of A, has a least upper bound and a greatest lower bound. |
| A. | Chain |
| B. | Lattice. |
| C. | Antichains |
| D. | Group |
| Answer» B. Lattice. | |
| 71. |
Pigeon Hole Principle says that if there are many pigeons and a few pigeon holes, then there must be some pigeon holes occupied by-------------- |
| A. | Two or more pigeons. |
| B. | Pigeons |
| C. | One only |
| D. | None |
| Answer» A. Two or more pigeons. | |
| 72. |
Digraph can be represented by----- |
| A. | Hasse diagrams |
| B. | Digraph |
| C. | Graph |
| D. | None |
| Answer» A. Hasse diagrams | |
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