What Do You Know About Lattices?

10 Questions | By Livyn | Last updated: Dec 11, 2017 | Total Attempts: 43

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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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