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Engineering Maths - Set Theory and Algebra - Partial Ordering Lattice and Boolean Algebra Online Exam Quiz

Important questions about Engineering Maths - Set Theory and Algebra - Partial Ordering Lattice and Boolean Algebra. Engineering Maths - Set Theory and Algebra - Partial Ordering Lattice and Boolean Algebra MCQ questions with answers. Engineering Maths - Set Theory and Algebra - Partial Ordering Lattice and Boolean Algebra exam questions and answers for students and interviews.

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

Options

A : 1,3

B : 1,5

C : 1,3,5

D : None of these

2. Hasse diagrams are drawn for

Options

A : partially ordered sets

B : lattices

C : boolean Algebra

D : none of these

3. A self-complemented, distributive lattice is called

Options

A : Boolean algebra

B : Modular lattice

C : Complete lattice

D : Self dual lattice

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

Options

A : 30

B : 15

C : 10

D : 6

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

Options

A : 3

B : 4

C : 5

D : None of these

6. Principle of duality is defined as

Options

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.

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

Options

A : same

B : lattices with same order

C : isomorphic

D : order-isomorphic

8. The absorption law is defined as

Options

A : a * ( a * b ) = b

B : a * ( a ⊕ b ) = b

C : a * ( a * b ) = a ⊕ b

D : a * ( a ⊕ b ) = a

9. 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.

Options

A : 1

B : n

C : n + 2

D : n !

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 ?

Options

A : L is a Poset

B : L is a boolean algebra

C : L is a lattice

D : none of these

11. If lattice (C ,≤) is a complemented chain, then

Options

A : |C|≤1

B : |C|≤2

C : |C| >1

D : C doesn't exist

12. The less than relation, <, on reals is

Options

A : a partial ordering since it is asymmetric and reflexive.

B : a partial ordering since it is anti-symmetric and reflexive.

C : not a partial ordering because it is not asymmetric and not reflexive

D : not a partial ordering because it is not anti- symmetric and not reflexive.

15. Let D 30 = (l, 2, 3, 5, 6, 10, 15,30) and relation I be a partial ordering on D 30 . The all upper bounds of 10 and 15 respectively is

Options

A : 30

B : 15

C : 10

D : 6

16. Let D 30 = 11,2,3,5,6, 10, 15,30) and relation I be a partial ordering on D 30 - The lub of 10 and 15 respectively is

Options

A : 30

B : 15

C : 10

D : 6

17. Complement of each element of D 6 in [D 6 ; v, ^], is

Options

A : 1' = 2, 2' = 3, 3' = 2, 6' = 1

B : 1'=6, 2'=3, 3'=6, 6'=1

C : 1' = 6, 6' = 1, 3' = 2, 2' = 3

D : none of these

18. Maximal and minimal elements of the Poset are

Options

A : Maximal 5, 6; Minimal 2

B : Maximal 5, 6; Minimal

C : Maximal 3, 5; Minimal 1, 6

D : None of these

19. The greatest and least elements of the Poset are

Options

A : greatest 4, 5; least 1, 2

B : greatest 5; least 1

C : greatest None; least none

D : none of these

20. The simultaneous equations on the Boolean variables x, y, z and w x+y+z= 1,                                                         xy = 0 xz+ w = 1,                                                    xy+zw = 0 have following solution for, x, y, z and w, respectively

Options

A : 0 1 0 0

B : 1 1 0 1

C : 1 0 1 1

D : 1 0 0 0

21. In the lattice defined by the Hasse diagram given below, how many complements does the element 'e' have?

Options

A : 2

B : 3

C : 0

D : 1

22. What values of A, B, G and D satisfy the following simultaneous boolean equations? A'+AB = 0, AB=AC, AB+AC'+CD = CD'

Options

A : A = 1, B = 0, C = 0, D = 1

B : A = 1, B = 1, C = 0, D = 0

C : A = 1, B = 0, C = 1, D = 1

D : A = 1, B = 0, C = 0, D = 0

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