What Do You Know About Lattices?

10 Questions | Total Attempts: 43

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What Do You Know About Lattices?

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).


Questions and Answers
  • 1. 
    Lattice is studied in ....?
    • A. 

      Mathematics

    • B. 

      English Language

    • C. 

      History

    • D. 

      Philosophy

  • 2. 
    Lattice consists of how many partially ordered set elements ?
    • A. 

      2

    • B. 

      3

    • C. 

      4

    • D. 

      1

  • 3. 
    The ......... is the only defining identity that is peculiar to lattice theory?
    • A. 

      Absorption law

    • B. 

      Law of physics

    • C. 

      Newton law

    • D. 

      Laws of power

  • 4. 
    The algebraic interpretation of lattices plays an essential role in ......?
    • A. 

      Vector space

    • B. 

      Polytopes

    • C. 

      Linear algebra

    • D. 

      Universal algebra

  • 5. 
    What is the smallest crystal lattice?
    • A. 

      Unit cell

    • B. 

      Primitive cell

    • C. 

      Lattice points

    • D. 

      Basis

  • 6. 
    In a bounded lattice the empty join and the empty meet can also be defined as ....?
    • A. 

      1 and 1

    • B. 

      0 and 1

    • C. 

      2 and 1

    • D. 

      0 and 0

  • 7. 
    Lattice has how many definitions?
    • A. 

      Two

    • B. 

      Three

    • C. 

      Four

    • D. 

      Five

  • 8. 
    Continous lattice is a complete lattice that is continuous as a .....?
    • A. 

      Supremum

    • B. 

      Infimum

    • C. 

      Poset

    • D. 

      Monoid

  • 9. 
    A/an ........ is a complete lattice that is algebraic as a poset?
    • A. 

      Heyting algebra

    • B. 

      Boolean algebra

    • C. 

      Algebraic lattice

    • D. 

      Linear lattice

  • 10. 
    In general, some elements of a ........ might not have a complement, and others might have more than one complement?
    • A. 

      Bounded lattice

    • B. 

      Algebraic lattice

    • C. 

      Continuous lattice

    • D. 

      Complete lattice

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