BCS Discrete Mathematics 3

Question 1

Which of the following statements about trees in graph theory is true?

Accepted Answer

A tree with n vertices has n-1 edges

Answer

A tree is a connected acyclic graph; a tree with n vertices always has exactly n-1 edges.

Question 2

What is 17 mod 5?

Accepted Answer

2

Answer

17 divided by 5 gives quotient 3 and remainder 2, so 17 mod 5 = 2.

Question 3

Which of the following correctly expresses De Morgan's law for sets?

Accepted Answer

(A ∪ B)' = A' ∩ B'

Answer

De Morgan's law for sets states (A ∪ B)' = A' ∩ B'; the complement of a union equals the intersection of complements.

Question 4

In how many ways can a committee of 3 be chosen from a group of 7 people?

Accepted Answer

35

Answer

Using combinations: C(7,3) = 7! / (3! × 4!) = 35, since the order of selection does not matter.

Question 5

Which quantifier asserts that a property holds for all elements in the domain?

Accepted Answer

Universal quantifier (∀)

Answer

The universal quantifier ∀ (for all) asserts that the given predicate is true for every element in the specified domain.

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