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Arithmetic Aptitude :: Sets, Relations and Functions

  1.  A Subset of B x B is called a

  2. A.

    Relation in A

    B.

    Relation in B

    C.

    Relation from A to B

    D.

    Relation from B to A


  3.  To draw general conclusions from well known facts is called

  4. A.

    Induction

    B.

    Deduction

    C.

    Proposition

    D.

    Knowledge


  5.  A declarative statement which may be true or false but not both is called

  6. A.

    Induction

    B.

    Deduction

    C.

    Knowledge

    D.

    Proposition


  7.  Set of Second element of ordered pair forming a relation is called its

  8. A.

    Range

    B.

    Domain

    C.

    Relation in A

    D.

    Relation in B


  9.  Which of the following statements is FALSE?

  10. A.

     2 ∈ A ∪ B implies that if 2 ∈/ A then 2 ∈ B. 

    B.

    {2, 3} ⊆ A implies that 2 ∈ A and 3 ∈ A.

    C.

    A ∩ B ⊇ {2, 3} implies that {2, 3} ⊆ A and {2, 3} ⊆ B

    D.

    {2} ∈ A and {3} ∈ A implies that {2, 3} ⊆ A.


  11.  Let A = {0, 1} × {0, 1} and B = {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is in alphabetic order. If A × B × A is listed in lexicographic order, then the next element

  12. A.

    ((1, 0), a,(0, 0))

    B.

    ((1, 1), c,(0, 0)) 

    C.

    ((1, 1), a,(0, 0))

    D.

    ((1, 1), a,(1, 1))


  13.  Which of the following statements is TRUE?

  14. A.

    For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.

    B.

    For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B ∪ C).

    C.

    For all sets A, B, and C, A − (B − C) = (A − B) − C.

    D.

    For all sets A, B, and C, if A ∪ C = B ∪ C then A = B. 


  15.  Which of the following statements is FALSE?

  16. A.

    A − (C ∪ B) = (A − B) − C

    B.

    B − (A ∪ C) = (B − C) − A

    C.

    C − (B ∪ A) = (C − B) − A

    D.

    A − (B ∪ C) = (B − C) − A


  17.  The power set P((A × B) ∪ (B × A)) has the same number of elements as the power set P((A × B) ∪ (A × B)) if and only if

  18. A.

    A = B

    B.

    A = ∅ or B = ∅

    C.

    B = ∅ or A = B

    D.

    A = ∅ or B = ∅ or A = B 


  19.  Let σ = 452631 be a permutation on {1, 2, 3, 4, 5, 6} in one-line notation (based on the usual order on integers). Which of the following is NOT a correct cycle notation for σ?

  20. A.

    (614)(532)

    B.

    (461)(352) 

    C.

    (253)(146)

    D.

    (325)(614)