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. |
Option: D Explanation : |
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 |
Option: D Explanation : |
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 |
Option: D Explanation : |
A partial order is deined on the set
S = {x, a_{1}, a_{2}, a_{3},...... a_{n}, y}
as x ≤ a i for all i and a_{i } ≤_{ } 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 ! |
Option: D Explanation : |
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 |
Option: C Explanation : |