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Arithmetic Aptitude :: Algebra Problems

  1.  Let D30 = {1, 2, 3, 4, 5, 6, 10, 15, 30} and relation I be partial ordering on D30. The all lower bounds of 10 and 15 respectively are

  2. A.

    1,5

    B.

    1,7

    C.

    1,3,5

    D.

    None of these

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  3.  Hasse diagrams are drawn for

  4. A.

    lattices

    B.

    boolean Algebra

    C.

    partially ordered sets

    D.

    none of these

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  5.  A self-complemented, distributive lattice is called

  6. A.

    Self dual lattice

    B.

    Complete lattice

    C.

    Modular lattice

    D.

    Boolean algebra

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  7.  Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30. The lub of 10 and 15 respectively is

  8. A.

    1

    B.

    5

    C.

    15

    D.

    30

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  9.  Let X = {2, 3, 6, 12, 24}, and ≤ be the partial order defined by X ≤ Y if X divides Y. Number of edges in the Hasse diagram of (X, ≤ ) is

  10. A.

    1

    B.

    3

    C.

    4

    D.

    7

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  11.  If lattice (C ,≤) is a complemented chain, then

  12. A.

    |C|≤2

    B.

    |C|≤1

    C.

    |C| >1

    D.

    C doesn't exist

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  13.  A self-complemented, distributive lattice is called

  14. A.

    Self dual lattice

    B.

    Modular lattice

    C.

    Complete lattice

    D.

    Boolean algebra

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  15.  The less than relation, <, on reals is

  16. A.

    not a partial ordering because it is not anti- symmetric and not reflexive.

    B.

    not a partial ordering because it is not asymmetric and not reflexive

    C.

    a partial ordering since it is anti-symmetric and reflexive.

    D.

    a partial ordering since it is asymmetric and reflexive.

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  17.  Principle of duality is defined as

  18. A.

    all properties are unaltered when  ≤ is replaced by ≥ other than 0 and 1 element.

    B.

    all properties are unaltered when  ≤ is replaced by ≥

    C.

    LUB becomes GLB

    D.

    ≤ is replaced by ≥

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  19.  Different partially ordered sets may be represented by the same Hasse diagram if they are

  20. A.

    same

    B.

    isomorphic

    C.

    order-isomorphic

    D.

    lattices with same order

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