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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

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

  4. A.

    Induction

    B.

    Deduction

    C.

    Proposition

    D.

    Knowledge

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

  6. A.

    Induction

    B.

    Deduction

    C.

    Knowledge

    D.

    Proposition

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  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

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  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.

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  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))

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  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. 

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  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

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  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 

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  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)

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