BCS Discrete Mathematics 2

Question 1

In propositional logic, which law states that P ∨ (Q ∧ R) ≡ (P ∨ Q) ∧ (P ∨ R)?

Accepted Answer

Distributive law

Answer

Absorption law

Answer

De Morgan's law

Answer

Associative law

Question 2

What is the greatest common divisor (GCD) of 48 and 36?

Accepted Answer

12

Answer

6

Answer

9

Answer

18

Question 3

Which of the following is a valid tautology?

Accepted Answer

P → P

Answer

P ∧ ¬P

Answer

P ∨ Q

Answer

P ∧ Q

Question 4

How many ways can 5 distinct books be arranged on a shelf?

Accepted Answer

120

Answer

25

Answer

60

Answer

720

Question 5

In graph theory, what is a Hamiltonian path?

Accepted Answer

A path that visits every vertex exactly once

Answer

A path that visits every edge exactly once

Answer

The shortest path between two vertices

Answer

A path that returns to the starting vertex

Question 6

What does the principle of mathematical induction require as its two steps?

Accepted Answer

Base case and inductive step

Answer

Base case and recursive case

Answer

Hypothesis and conclusion

Answer

Axiom and theorem

Question 7

Which set operation produces elements that are in either set A or set B but not in both?

Accepted Answer

Symmetric difference (A △ B)

Answer

Union (A ∪ B)

Answer

Intersection (A ∩ B)

Answer

Difference (A − B)