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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


  3.  Hasse diagrams are drawn for

  4. A.

    lattices

    B.

    boolean Algebra

    C.

    partially ordered sets

    D.

    none of these


  5.  A self-complemented, distributive lattice is called

  6. A.

    Self dual lattice

    B.

    Complete lattice

    C.

    Modular lattice

    D.

    Boolean algebra


  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


  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


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

  12. A.

    |C|≤2

    B.

    |C|≤1

    C.

    |C| >1

    D.

    C doesn't exist


  13.  A self-complemented, distributive lattice is called

  14. A.

    Self dual lattice

    B.

    Modular lattice

    C.

    Complete lattice

    D.

    Boolean algebra


  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.


  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 ≥


  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