What defines a planar graph?
A Can be drawn on a plane without crossing edges
B No edges
C No cycles
D Only directed edges
Which of the following is true about a logic gate?
A Mathematical operation
B Performs logical functions
C Generates random outputs
D Models physical processes
What is the output of an AND gate when both inputs are 1?
A 0
B 1
C Undefined
D 2
What is the primary objective of combinatorial optimization?
A Minimize costs
B Maximize profits
C Find the optimal solution for a problem
D Solve equations
What is the purpose of a Karnaugh map in Boolean algebra?
A Simplify Boolean expressions
B Solve linear equations
C Draw truth tables
D Perform logical operations
Which of the following is an example of a combinatorial optimization problem?
A Sorting a list
B Traveling salesman problem
C Solving linear equations
D Matrix multiplication
In graph theory, what is the chromatic number of a graph?
A Number of edges
B Number of vertices
C Minimum number of colors needed for coloring the graph
D Degree of the graph
What is a binary tree in computer science?
A A tree with two branches
B A tree with no nodes
C A tree with one root and up to two children per node
D A directed acyclic graph
What is a convex polygon?
A A polygon with all interior angles less than 180°
B A polygon with all sides equal
C A polygon with no edges
D A polygon with one interior angle greater than 180°
What does De Morgan’s law state about Boolean expressions?
A Describes properties of logic gates
B Relates AND and OR operations to NOT
C Simplifies truth tables
D Converts expressions to standard form
In decision theory, what is a decision tree used for?
A Visualizing algorithms
B Evaluating the outcomes of different decisions
C Calculating probabilities
D Mapping functions
What is the main feature of a planar graph?
A All edges intersect
B It can be drawn without edge crossings
C It has no vertices
D It contains no edges
What is a non directed graph?
A A graph with directed edges
B A graph without any cycles
C A graph where edges have no direction
D A graph with no vertices
What is a Hamiltonian path in a graph?
A A path that visits every edge
B A path that visits every vertex exactly once
C A cycle that visits all vertices
D A cycle with a maximum number of edges
What is an XOR gate in Boolean logic?
A AND of inputs
B OR of inputs
C Exclusive OR, true if only one input is true
D NOT of inputs