Lecture 10 - Proofs (Part 2)

These flashcards cover key concepts related to logic and algorithms, focusing on proving statements, types of integers, and methods of proof.

Proof by Contrapositive

A method of proving that an implication is true by demonstrating that if the conclusion is false, then the hypothesis must also be false.

Contrapositive

The contrapositive of a statement p → q is ¬q → ¬p, which is logically equivalent to the original implication.

Theorem

A statement proven to be true through deductive reasoning.

Even Integer

An integer that is divisible by 2 without a remainder.

Odd Integer

An integer that is not divisible by 2, resulting in a remainder of 1.

Logical Equivalence

Two statements that are either both true or both false in every possible scenario.

Assumption in Proof

A statement assumed to be true for the purpose of deriving a conclusion in a logical argument.

Proof Example

A specific instance or case used to illustrate how a theorem or statement is proved.

Subtracting Equations

A mathematical operation that involves taking one equation away from another to simplify or solve for unknown variables.

Dividing Equations

A mathematical operation involving dividing both sides of an equation by the same non-zero number to find unknown values.