DISCRETE MATHS TEST QUESTIONS
WITH REVISED AND UPDATED
ANSWERS
Mutually exclusive vs independent - Answer-Two events are mutually exclusive if A∩B =
∅ (they cannot occur simultaneously)
Independent is when the occurrence of one does not influence the occurrence of the
other
Probability of event A - Answer-P(A) = the sum of the probabilities of the elements in A
What is P(AUB) if A and B are mutually exclusive? - Answer-P(A)+P(B)
P(A|B) - Answer-P(A∩B)/P(B)
How to check if A and B are independent - Answer-If P(A∩B) = P(A)*P(B)
When does a connected graph with =>1 edge have a Euler cycle? - Answer-If and only
if it has no vertices of odd degree
What is a Euler cycle? - Answer-A cycle in a graph G that includes all of the edges and
all of the vertices of G
Konigsberg Bridge Problem - Answer-Two islands in a river were connected to each
other and the land by 7 bridges. Is it possible for a parade to cross each of the 7 bridges
once and only once during the walk to town
Four Color Problem - Answer-Is it possible to color every map with 4 colors so that no
two adjacent countries are colored the same?
Marriage Theorem - Answer-If every girl in a village knows k boys and every boy knows
k girls, then each girl can marry a boy she knows and each boy can amrry a girl he
knows
e = {u, v}, edge notation? - Answer-uv or vu
Multigraphs (undirected graphs) - Answer-Allow loops (edges joining a vertex to itself)
and parallel edges (several edges joining the same two vertices)
Digraphs (directed graphs) - Answer-Ordered pair of vertices
WITH REVISED AND UPDATED
ANSWERS
Mutually exclusive vs independent - Answer-Two events are mutually exclusive if A∩B =
∅ (they cannot occur simultaneously)
Independent is when the occurrence of one does not influence the occurrence of the
other
Probability of event A - Answer-P(A) = the sum of the probabilities of the elements in A
What is P(AUB) if A and B are mutually exclusive? - Answer-P(A)+P(B)
P(A|B) - Answer-P(A∩B)/P(B)
How to check if A and B are independent - Answer-If P(A∩B) = P(A)*P(B)
When does a connected graph with =>1 edge have a Euler cycle? - Answer-If and only
if it has no vertices of odd degree
What is a Euler cycle? - Answer-A cycle in a graph G that includes all of the edges and
all of the vertices of G
Konigsberg Bridge Problem - Answer-Two islands in a river were connected to each
other and the land by 7 bridges. Is it possible for a parade to cross each of the 7 bridges
once and only once during the walk to town
Four Color Problem - Answer-Is it possible to color every map with 4 colors so that no
two adjacent countries are colored the same?
Marriage Theorem - Answer-If every girl in a village knows k boys and every boy knows
k girls, then each girl can marry a boy she knows and each boy can amrry a girl he
knows
e = {u, v}, edge notation? - Answer-uv or vu
Multigraphs (undirected graphs) - Answer-Allow loops (edges joining a vertex to itself)
and parallel edges (several edges joining the same two vertices)
Digraphs (directed graphs) - Answer-Ordered pair of vertices
