Discrete Mathematics Quiz

What is the cardinality of the power set of a set with $ n $ elements?

• $ n $

• $ 2^n $

• $ n^2 $

• $ n! $

Which of the following is NOT a valid logical connective?

• AND

• OR

• IF-THEN

• WITH

In a directed graph, the sum of in-degrees equals the sum of out-degrees because:

• The graph is symmetric.

• Each edge contributes one in-degree and one out-degree.

• There are no isolated vertices.

• The graph is bipartite.

What is the complement of the union of two sets $ A $ and $ B $?

• $ A^c \cap B^c $

• $ A^c \cup B^c $

• $ (A \cap B)^c $

• $ (A \cup B)^c $

Tags

CCSS.HSS.CP.A.1

The negation of the statement "If $ P $, then $ Q $" is:

• $ \neg P \wedge Q $

• $ P \wedge \neg Q $

• $ P \rightarrow Q $

• $ \neg P \vee Q $

A relation $ R $ on a set $ A $ is a function if:

• Each element of $ A $ is related to exactly one element of $ A $.

• $ R $ is reflexive.

• $ R $ is symmetric.

• $ R $ is transitive.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Which of the following is NOT a property of equivalence relations?

• Reflexivity

• Symmetry

• Transitivity

• Injectivity

The number of edges in a complete graph $ K_n $ is:

• $ n $

• $ n(n-1) $

• $ \frac{n(n-1)}{2} $

• $ 2^n $

In a propositional logic formula, $ P \wedge \neg P $ is always:

• True

• False

• Undefined

• Depends on $ P $

Which of the following is a tautology?

• $ P \wedge Q $

• $ P \vee \neg P $

• $ P \wedge \neg P $

• $ \neg P \vee Q $