COMP 283 Final 2026 (85 Questions) – Discrete Mathematics, Graph Theory, Induction & Probability Complete Q&A

This document contains approximately 85 final exam questions with verified answers for COMP 283 Final 2026 . The material comprehensively covers formal languages and set notation (membership in sets, Kleene star operations, union, concatenation), logical reasoning, and multiple variations of mathematical induction, including validity of induction rules over natural numbers and integers. It also evaluates well-founded relations and foundational proof techniques used in discrete mathematics. A major portion of the document focuses on graph theory, including planarity (K₅ and K₃,₃), properties of trees, bipartite graphs, Eulerian and Hamiltonian paths, graph coloring, cliques, complete graphs, connected components, and structural properties of planar graphs. It also includes combinatorics problems such as counting cliques and ordered binary trees, along with applications of Euler’s formula for planar graphs. The exam further covers probability theory and discrete random variables, including independent and mutually exclusive events, expected value calculations, coin toss and dice roll probability, binomial expectations, geometric expectations, Markov-style inequalities, and combinatorial probability scenarios. Questions require conceptual understanding as well as computational accuracy, reflecting a rigorous upper-level discrete mathematics or introductory theory of computation course. This document is highly relevant for courses such as Discrete Mathematics, Foundations of Computer Science, Graph Theory, Combinatorics, Probability for Computer Science, and Theory of Computation. It is ideal for computer science majors, software engineering students, mathematics students, and anyone preparing for a cumulative discrete structures final exam. Keywords: discrete mathematics, formal languages, kleene star, set membership, mathematical induction, well founded relation, graph theory, planar graphs, k5 non planar, k33 non planar, trees and bipartite graphs, eulerian path, hamiltonian path, graph coloring, cliques counting, combinatorics counting, probability theory, expected value discrete, independent events probability, binomial expectation, geometric distribution expectation