BSCS Discrete Mathematics and Logic

Question 1

What is a proposition in propositional logic?

Accepted Answer

A statement that is either true or false

Answer

A proposition is a declarative statement that has a definite truth value — it is either true or false, not both.

Question 2

What does the logical connective ¬ (NOT) do?

Accepted Answer

Negates the truth value of a proposition

Answer

The NOT operator negates a proposition: if P is true, ¬P is false, and vice versa.

Question 3

What is the cardinality of the set {a, b, c, d}?

Accepted Answer

4

Answer

The cardinality of a set is the number of elements it contains; {a, b, c, d} has 4 elements.

Question 4

Which of the following represents a tautology?

Accepted Answer

P ∨ ¬P

Answer

P ∨ ¬P is always true regardless of P's value — it is a tautology known as the Law of Excluded Middle.

Question 5

What is the Pigeonhole Principle?

Accepted Answer

If n+1 items are put into n containers, at least one container has more than one item

Answer

The Pigeonhole Principle states that if n+1 items are placed into n containers, at least one container must hold at least two items.

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