## Discrete Mathematics Solved MCQs

**1. The function q ∨ r is equal to the function:**

A. ((p ∨ r) ∨ q) ∧ (p ∨ r)

B. (p ∧ q) ∨ (p ∧ r)

C. (p ∨ q) ∧ ∼(p ∨ r)

D. (p ∨ (r ∨ q)) ∧ ∼(∼q ∧ ∼r)

**2. The truth table for (p ∨ q) ∨ (p ∧ r) is the same as the truth table for:**

A. p ∨ q

B. (p ∨ q) ∧ r

C. (p ∨ q) ∧ (p ∧ r)

D. (p ∨ q) ∧ (p ∨ r)

**3. How many have all the vowels together in word MISAPPREHENSION:**

A. 15!/2!2!2!2!2!

B. 10!/2!2!2! × 6!/2!2!

C. 13!/2!2!2!2!

D. None of the above

**4. The Boolean function [∼(∼p∧q)∧∼(∼p∧∼q)]∨(p∧r) is equal to the Boolean function:**

A. q

B. p ∧ r

C. p

D. None of the above

**5. In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities? **

A. 123

B. 220

C. 130

D. 120

**6. Which of the following statements is FALSE:**

A. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to ∼Q ∧ ∼P

B. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ P

C. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to Q ∨ (P ∧ ∼Q)

D. (P ∧ Q) ∨ (∼P ∧ Q) ∨ (P ∧ ∼Q) is equal to [(P ∨ ∼P) ∧ Q] ∨ (P ∧ ∼Q)

**7. In any, undirected graph the sum of degrees of all the nodes**

A. Must be even

B. Are twice the number of edges

C. Must be odd

D. Need not be even

**8. The walk of a graph length is: **

A. The number of vertices in walk W

B. Total number of vertices in a graph

C. Total number of edges in a graph

D. The number of edges in walk W

**9. Definition of a plane graph is:**

A. A graph, drawn in a plane in such a way that any pair of edges meet only at their end vertices

B. A graph, drawn in a plane in such a way that if the vertex set of the graph can be partitioned into two non – empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y

C. A simple graph which is Isomorphic to Hamiltonian graph

D. None of the above

**10. A continuous non-intersecting curve in the plane whose origin and terminus coincide :**

A. Jordan

B. Planer

C. Hamiltonian

D. All of these

**11. V is an isolated vertex in a graph, then the degree of v is: **

A. 2

B. 1

C. 0

D. 3

12. Hasse diagrams are drawn

A. Partially ordered sets

B. Lattices

C. Boolean algebra

D. None of these