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Arithmetic Aptitude :: Sets, Relations and Functions

  1.  If every element of a group G is its own inverse, then G is

  2. A.

    abeian

    B.

    cyclic

    C.

    finite

    D.

    infinite

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  3.  The universal relation A x A on A is

  4. A.

    anti-symmetric

    B.

    an equivalence relation

    C.

    a partial ordering relation

    D.

    not symmetric and not anti-symmetric

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  5.  Total number of diferent partitions of a set having four elements is

  6. A.

    5

    B.

    10

    C.

    15

    D.

    20

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  7.  A partition of {1, 2, 3, 4, 5} is the family

  8. A.

    {(1, 2, 3),(5)}

    B.

    {(1, 2,), (3, 4, 5)}

    C.

    {φ(1, 2),(3, 4),(5)}

    D.

    {(1, 2),(3, 4),(3, 5)}

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  9.  Let s(w) denote the set of all the letters in w where w is an English word. Let us denote set equality, subset and union relations by =, ⊂ and ∪ respectively. Which of the following is NOT true?

  10. A.

    s(ten) ⊂ s(twenty)

    B.

    s(stored) = s(sorted)

    C.

    s(sixty) ⊂ (s(six)  ∪ s(twenty)

    D.

    None of these

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  11.  In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ?

  12. A.

    18

    B.

    24

    C.

    36

    D.

    44

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  13.  Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?

  14. A.

    p x q

    B.

    p + q

    C.

    2 pq

    D.

    4 pq

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  15.  The set of all Equivalence classes of a set A of cardinality C

  16. A.

    forms a partition of A

    B.

    is of cardinality 2C

    C.

    has the same cardinality as A

    D.

    none of these

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  17.  Let Z denote the set of all integers. Define f : Z —> Z by f(x) = {x / 2 (x is even) 0 (x is odd) then f is

  18. A.

    one-one and onto

    B.

    one-one but not onto

    C.

    onto but not one-one

    D.

    neither one-one nor-onto

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  19.  Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is

  20. A.

    partial order

    B.

    equivalence relation

    C.

    symmetric but not transitive

    D.

    anti symmetric and not transitive

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