Classical

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

1:  

Let D30 = {1, 2, 3, 4, 5, 6, 10, 15, 30} and relation I be partial ordering on D30. The all lower bounds of 10 and 15 respectively are

A.

1,3

B.

1,5

C.

1,3,5

D.

None of these

 
 

Option: B

Explanation :


2:  

 Hasse diagrams are drawn for

A.

partially ordered sets

B.

lattices

C.

boolean Algebra

D.

none of these

 
 

Option: D

Explanation :


3:  

A self-complemented, distributive lattice is called

A.

Boolean algebra

B.

Modular lattice

C.

Complete lattice

D.

Self dual lattice

 
 

Option: A

Explanation :


4:  

 Let  D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30. The lub of 10 and 15 respectively is

A.

30

B.

15

C.

10

D.

6

 
 

Option: A

Explanation :


5:  

Let X = {2, 3, 6, 12, 24}, and ≤ be the partial order defined by X Y if X divides Y. Number of edges in the Hasse diagram of (X,   ) is

A.

3

B.

4

C.

5

D.

None of these

 
 

Option: B

Explanation :




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