Set Theory and Algebra MCQ - Partial Ordering , Lattice and Boolean Algebra

6:

Principle of duality is defined as

 A. ≤ is replaced by ≥ B. LUB becomes GLB C. all properties are unaltered when  ≤ is replaced by ≥ D. all properties are unaltered when  ≤ is replaced by ≥ other than 0 and 1 element. Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
7:

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

 A. same B. lattices with same order C. isomorphic D. order-isomorphic Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
8:

The absorption law is defined as

 A. a  * ( a * b ) = b B. a * ( a ⊕ b ) = b C. a * ( a * b ) = a ⊕ b D. a * ( a ⊕ b ) = a Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
9:

A partial order is deined on the set

S = {x, a1, a2, a3,...... an, y}

as x ≤  a i for all i and ai     y for all i, where n  ≥ 1.

Number of total orders on the set S which contain partial order  ≤ is

 A. 1 B. n C. n + 2 D. n ! Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
10:

Let L be a set with a relation R which is transitive, antisymmetric and reflexive and for any two elements a, b  ∈ L. Let least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist. Which of the following is/are TRUE ?

 A. L is a Poset B. L is a boolean algebra C. L is a lattice D. none of these Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:

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