What does set theory deal with?
A Collections of objects
B Numbers
C Groups
D Logical operations
What is a logical proposition?
A A number
B A statement that is either true or false
C A mathematical equation
D A decision rule
What does the logical AND operator represent in Boolean logic?
A Either input is true
B Only one input is true
C Both inputs are true
D None of the inputs are true
What is a relation in mathematics?
A A set of ordered pairs
B A set of numbers
C A logical operation
D A mathematical function
In graph theory, what is a vertex?
A A point where edges meet
B A point where edges meet
C A line
D A loop
What is a function in mathematics?
A A set of rules
B A set of ordered pairs
C A mapping from one set to another
D A sum of numbers
What does the distributive property in Boolean algebra state?
A AND distributes over OR
B OR distributes over AND
C OR distributes over NOT
D NOT distributes over AND
What is a recurrence relation?
A A function of multiple variables
B A relation between elements of a sequence
C A rule for defining probabilities
D A graph of points
What is the purpose of a truth table?
A To solve equations
B To represent logical operations
C To create functions
D To perform set operations
In network flows, what does the capacity of an edge represent?
A The maximum possible flow through the edge
B The weight of the edge
C The number of vertices connected
D The direction of flow
What is a randomized algorithm?
A An algorithm with fixed outcomes
B An algorithm using random decisions for solving problems
C An algorithm that always produces the same result
D An algorithm based on recursion
What is the key property of a planar graph?
A It has no vertices
B It can be drawn on a plane without edge crossings
C It contains cycles
D It contains only directed edges
What does the minimum cut in a flow network represent?
A The total flow capacity
B The smallest set of edges separating the source and sink
C The maximum flow from source to sink
D The largest flow path
What is the purpose of a minimum spanning tree in graph theory?
A To connect all vertices with the least total edge weight
B To find cycles in a graph
C To find the maximum flow
D To reduce graph complexity
What does a Hamiltonian cycle do in a graph?
A Visits every edge
B Visits each vertex once and returns to the starting point
C Finds the shortest path
D Makes a path of maximum length