Classical

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.

 
 

Option: D

Explanation :


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

 
 

Option: D

Explanation :


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

 
 

Option: D

Explanation :


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.

!

 
 

Option: D

Explanation :


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

 
 

Option: C

Explanation :




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