What is a mathematical or logical name for the process of proving a statement by exhausting the domain?

Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the …

What is logic and proof in mathematics?

proof, in logic, an argument that establishes the validity of a proposition. Although proofs may be based on inductive logic, in general the term proof connotes a rigorous deduction.

What does deductive mean in math?

“Deductive reasoning” refers to the process of concluding that something must be true because it is a special case of a general principle that is known to be true. … Deductive reasoning is logically valid and it is the fundamental method in which mathematical facts are shown to be true.

What is inductive logic in philosophy?

An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data.

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How can you prove that a proposition is true?

Essentially, we prove a statement of the form ¬p ⇒ q, where q is never true. Since q cannot be true, we also cannot have ¬p is true, since ¬p ⇒ q. Therefore, if ¬p is false, we must have that p is true, completing the proof of proposition p.

What is logic in math examples?

For example, 1 + 2 = 3 and 4 is even are clearly true, while all prime numbers are even is false. In logic we are often not interested in these statements themself, but how true and false statements are related to each other.
Propositional Calculus.

P Q P ∧ Q

What makes a statement logical?

A logical statement is a statement that, when true, allows us to take a known set of facts and infer (or assume) a new fact from them.

How do you prove a statement in math?

Methods of proof

  1. Direct proof.
  2. Proof by mathematical induction.
  3. Proof by contraposition.
  4. Proof by contradiction.
  5. Proof by construction.
  6. Proof by exhaustion.
  7. Probabilistic proof.
  8. Combinatorial proof.

What is proposition in math?

A proposition is a statement that is either true or false. In our course, we will usually call a mathematical proposition a theorem. A theorem is a main result. A proposition that is mainly of interest to prove a larger theorem is called a lemma. Some intermediate results are called propositions.

What is tautology math?

A tautology is a compound statement in Maths which always results in Truth value. It doesn’t matter what the individual part consists of, the result in tautology is always true.

What are the five logical connectives?

Commonly used connectives include “but,” “and,” “or,” “if . . . then,” and “if and only if.” The various types of logical connectives include conjunction (“and”), disjunction (“or”), negation (“not”), conditional (“if . . . then”), and biconditional (“if and only if”).

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What is contingency in mathematical logic?

In philosophy and logic, contingency is the status of propositions that are neither true under every possible valuation (i.e. tautologies) nor false under every possible valuation (i.e. contradictions). A contingent proposition is neither necessarily true nor necessarily false.

What is contradiction in mathematical logic?

In Mathematics, a contradiction occurs when we get a statement p, such that p is true and its negation ~p is also true. Now, let us understand the concept of contradiction with the help of an example.

How do you prove exhaustion?

For the case of Proof by Exhaustion, we show that a statement is true for each number in consideration (or subsets of numbers). Proof by Exhaustion also includes proof where numbers are split into a set of exhaustive categories and the statement is shown to be true for each category.

What is logical equivalence in discrete mathematics?

Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra. You can’t get very far in logic without talking about propositional logic also known as propositional calculus.