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

The distributive law in propositional logic allows OR to distribute over AND (and vice versa), giving P ∨ (Q ∧ R) ≡ (P ∨ Q) ∧ (P ∨ R).

Question 2

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

Accepted Answer

12

Answer

Using the Euclidean algorithm: GCD(48, 36) = GCD(36, 12) = GCD(12, 0) = 12.

Question 3

Which of the following is a valid tautology?

Accepted Answer

P → P

Answer

P → P (P implies P) is always true regardless of the truth value of P, making it a tautology.

Question 4

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

Accepted Answer

120

Answer

The number of permutations of 5 distinct objects is 5! = 5×4×3×2×1 = 120.

Question 5

In graph theory, what is a Hamiltonian path?

Accepted Answer

A path that visits every vertex exactly once

Answer

A Hamiltonian path visits every vertex in a graph exactly once; it does not need to return to the starting vertex.

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