Discrete Mathematics

Proving Program Correctness: Assertions and Loop Invariants 📘 Overview Program correctness connects a program’s execution to explicit preconditions and postconditions. Assertio...

Strong Induction 📘 Overview Strong induction proves an integer-indexed claim by assuming it holds at every earlier index when establishing the next case. It is especially suite...

Proof by Cases and Counterexamples 📘 Overview Proof by cases establishes a claim by proving it under every possibility in an exhaustive case split. A counterexample disproves a...

Mathematical Induction 📘 Overview Mathematical induction proves that a statement holds for every integer from a specified starting point onward. In computing, it supports proof...

Counting: Sum and Product Rules, Permutations and Combinations 📘 Overview Counting determines how many outcomes a situation has without listing them one by one. The sum rule an...

Proof by Contradiction 📘 Overview Proof by contradiction establishes a claim by showing that its negation leads to an impossibility. In computing, it supports proofs about algo...

Proof by Contraposition 📘 Overview Proof by contraposition establishes a conditional statement by proving its logically equivalent contrapositive. In computing, it is useful wh...