Relations MCQ

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• Which of the following is an equivalence relation on R, for a, b ∈ Z?
  ক

  (a-

  খ

  ∈ Z [ (a2+

  গ

  ∈ Z [ (ab+c

  ঘ

  /2 ∈ Z [ (2c3)/3 ∈ Z
• For a, b ∈ Z define a | b to mean that a divides b is a relation which does not satisfy ___________
  ক

  irreflexive and symmetric relation

  খ

  reflexive relation and symmetric relation

  গ

  transitive relation

  ঘ

  symmetric relation
• Determine the number of possible relations in an antisymmetric set with 19 elements.
  ক

  23585

  খ

  2.02 * 1087

  গ

  9.34 * 791

  ঘ

  35893
• 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?
  ক

  Every non-empty subset of has a greatest lower bound

  খ

  It is uncountable

  গ

  Every non-empty finite subset of has a least upper bound

  ঘ

  Every non-empty subset of has a least upper bound
• 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 ___________
  ক

  | is an equivalence relation

  খ

  It is a total order

  গ

  Every subset of N has an upper bound under |

  ঘ

  (N,|) is a lattice but not a complete lattice
• 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 ______
  ক

  (145, 265) and (0, 153)

  খ

  ∊ 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 ______ a) (145, 265) and (0, 153) [ (22, 101) and (0, 153)

  গ

  (101, 22) and (145, 265)

  ঘ

  (101, 22) and (0, 153)
• If the longest chain in a partial order is of length l, then the partial order can be written as _____ disjoint antichains.
  ক

  l2

  খ

  l+1

  গ

  l

  ঘ

  ll
• If A, B and C are any three sets, then A × (B ∪ C) is equal to _____________
  ক

  (A × B) ∪ (A × C)

  খ

  (A × B) ∩ (A × C)

  গ

  (A ∪ B) × (A ∪ C)

  ঘ

  None of the mentioned
• If A and B are any two sets, then A ∪ (A ∩ B) is equal to _____________
  ক

  A

  খ

  B

  গ

  A^C

  ঘ

  B^C
• If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then?
  ক

  A=B

  খ

  A=C

  গ

  B=C

  ঘ

  A=B=C
• If A, B and C are any three sets, then A – (B ∪ C) is equal to _____________
  ক

  (A – B) ∪ (A – C)

  খ

  (A – B) ∪ C

  গ

  (A – B) ∩ (A – C)

  ঘ

  (A – B) ∩ C
• Empty set is a _____________
  ক

  Invalid set

  খ

  Infinite set

  গ

  Finite set

  ঘ

  None of the mentioned
• If A ∩ B = B, then?
  ক

  A ⊂ B

  খ

  A = ø

  গ

  B ⊂ A

  ঘ

  B = ø
• If a set A has n elements, then the total number of subsets of A is?
  ক

  N

  খ

  2n

  গ

  N2

  ঘ

  2n
• If every aRb and bRc implies aRc, then the relation is transitive.
  ক

  True

  খ

  False
• If every aRb implies bRa then a relation R will be a symmetric relation.
  ক

  True

  খ

  False
• R is said to be reflexive if aRa is true for every a in A.
  ক

  True

  খ

  False
• (a,b) what is b?
  ক

  Domain

  খ

  what is b? a) Domain [ Range

  গ

  Domain & Range

  ঘ

  None of the mentioned
• (a,b) what is a?
  ক

  Domain

  খ

  what is a? a) Domain [ Range

  গ

  Domain & Range

  ঘ

  None of the mentioned