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PMIST-Discrete Mathematical Structures MCQs – U24MA203

Total questions: 50

Worksheet time: 25mins

Name
Class
Date
1.

Which of the following is a tautology?

a)

p ∧ ¬p

b)

p ∨ ¬p

c)

p ⇒ q

d)

¬p ∧ q

2.

What is the negation of the statement p ∨ q?

a)

¬p ∧ ¬q

b)

¬p ∨ ¬q

c)

p ∧ q

d)

¬p ∨ q

3.

Which connective represents 'if and only if' in logic?

a)

∧

b)

∨

c)

→

d)

↔

4.

The dual of p ∧ (q ∨ r) is:

a)

p ∨ (q ∧ r)

b)

p ∧ (q ∧ r)

c)

¬p ∨ ¬(q ∧ r)

d)

¬p ∧ ¬(q ∨ r)

5.

What is a well-formed formula?

a)

A Formula with no connectives

b)

Balanced parentheses and valid syntax

c)

any statement including connectives

d)

none of the above

6.

Truth tables are primarily used to determine:

a)

Number of propositions

b)

Truth value of a compound statement

c)

Notation of logic

d)

Negation of statements

7.

Which law states that p ∨ q ≡ ¬(¬p ∧ ¬q)?

a)

Distributive

b)

De Morgan’s

c)

Associative

d)

Commutative

8.

The conditional statement p ⇒ q is logically equivalent to:

a)

¬p ∨ q

b)

p ∧ ¬q

c)

¬q ⇒ ¬p

d)

q ⇒ p

9.

Disjunctive normal form means:

a)

Conjunction of disjunctions

b)

Disjunction of conjunctions

c)

Negation of formulas

d)

None of the above

10.

Truth table value of p ∧ (p ∨ q) when p is true and q is false?

a)

True

b)

False

c)

Undefined

11.

The power set of {a,b} contains how many elements?

a)

2

b)

3

c)

4

d)

8

12.

Which operation corresponds to A ∩ B?

a)

Union

b)

Intersection

c)

Complement

d)

Cartesian product

13.

What is the Cartesian product A × B if A={1,2} and B={x,y}?

a)

(1,2), (x,y)

b)

(1,x), (1,y), (2,x), (2,y)

c)

{1,2,x,y}

d)

(x,1), (y,2)

14.

Which is true?

a)

A ⊆ A

b)

A ⊆ ∅

c)

∅ ⊆ A

d)

Both a and c

15.

The complement of the universal set U is:

a)

U

b)

∅

c)

UcU^c

16.

The power set of set S always contains:

a)

S itself

b)

The empty set

c)

Both a and b

d)

Only subsets of size 1

17.

Using Venn diagrams, area representing A ∪ B:

a)

Only A

b)

Only B

c)

A, B or both

d)

Outside A and B

18.

If A = {1,2}, B = {2,3}, what is A ∪ B?

a)

{1,2}

b)

{2,3}

c)

{1,2,3}

d)

{1,3}

19.

An n-tuple is:

a)

Unordered collection

b)

Set with repeats

c)

Ordered n elements

d)

None

20.

Principle of specification restricts:

a)

Size of set

b)

Formation by predicates

c)

Basic operations

d)

None

21.

A relation from A to B is a subset of:

a)

A

b)

B

c)

A × B

d)

None

22.

Which is NOT a binary relation property?

a)

Reflexivity

b)

Transitivity

c)

Commutativity

d)

Symmetry

23.

The relation matrix represents:

a)

Membership

b)

Properties

c)

Elements and relation

d)

None

24.

The relation 'is equal to' is:

a)

Equivalence

b)

Partial order

c)

Compatibility

d)

None

25.

Partial ordering means:

a)

Reflexive, antisymmetric, transitive

b)

Reflexive, symmetric, transitive

c)

Irreflexive

d)

None

26.

Which relation partitions into equivalence classes?

a)

Reflexive only

b)

Symmetric only

c)

Equivalence

d)

Partial order

27.

Composition of R and S is:

a)

R ∪ S

b)

R ∩ S

c)

{ (a,c) | ∃b, (a,b) ∈ R ∧ (b,c) ∈ S }

d)

None

28.

A partially ordered set is a:

a)

Lattice

b)

Poset

c)

Group

d)

None

29.

Compatibility relations ensure:

a)

Related to itself

b)

If aRb, a and b compatible

c)

Symmetry

d)

None

30.

Antisymmetric relation example:

a)

Equality

b)

Strict inequality

c)

Subset relation

d)

Both a and c

31.

Which of the following does a graph consist of?

a)

Vertices only

b)

Edges only

c)

Vertices and edges

d)

None

32.

In an Eulerian graph, every vertex has:

a)

Even degree

b)

Odd degree

c)

Degree 1

d)

Degree 0

33.

What is a Hamiltonian path?

a)

Visits every vertex once

b)

Visits each edge once

c)

Cycle without repetition

d)

None

34.

Traveling Salesman Problem relates to:

a)

Euler paths

b)

Shortest Hamiltonian cycle

c)

Connected components

d)

None

35.

NOT a walk type:

a)

Path

b)

Circuit

c)

Tour

d)

Cycle

36.

A connected graph has:

a)

Isolated vertex

b)

Path between every pair

37.

Edge removal from graph:

a)

Deletion

b)

Contraction

c)

Subdivision

d)

None

38.

Subgraphs contain:

a)

All vertices/edges

b)

Some vertices/edges

c)

Only isolated vertices

d)

None

39.

Euler’s formula for planar graphs:

a)

V - E + F = 2

b)

V + E = F

c)

E - V + F = 0

d)

None

40.

Operation merging two vertices by edge:

a)

Deletion

b)

Contraction

c)

Subdivision

d)

None

41.

A tree is:

a)

Connected graph with cycles

b)

Connected acyclic graph

c)

disconnected graph

d)

none

42.

Pendant vertices are:

a)

Degree 1

b)

Degree 2

c)

Connected to all

d)

None

43.

The center of a tree is:

a)

Minimize max distance

b)

Highest degree

c)

Root vertex

d)

None

44.

Rooted trees differ:

a)

Special root vertex

b)

Have cycles

c)

Disconnected

d)

None

45.

Spanning trees of complete graph K_n:

a)

nn−2n^{n-2}

b)

n!

c)

2n2^n

d)

None

46.

Kruskal's algorithm finds:

a)

Eulerian paths

b)

Minimal spanning trees

c)

Detect cycles

d)

Hamiltonian cycles

47.

Weighted graph shortest spanning tree:

a)

Min total weight

b)

Max edges

c)

Max weight sum

d)

None

48.

A binary tree has:

a)

At most 2 children

b)

2 parents

c)

No children

d)

None

49.

Fundamental circuit is formed by:

a)

Add edge to spanning tree

b)

Remove edge

c)

Cycle

d)

None

50.

Distance in a tree:

a)

# edges in shortest path

b)

Sum of degrees

c)

# vertices

d)

None

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