Ads
related to: contraposition of a statement examples in geometry classkutasoftware.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as ...
Proof by contraposition infers the statement "if p then q" by establishing the logically equivalent contrapositive statement: "if not q then not p". For example, contraposition can be used to establish that, given an integer x {\displaystyle x} , if x 2 {\displaystyle x^{2}} is even, then x {\displaystyle x} is even:
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
Direct proof. In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established facts, usually axioms, existing lemmas and theorems, without making any further assumptions. [1] In order to directly prove a conditional statement of the form "If p, then q ", it ...
Tautology (logic) In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of ...
For example, given a formula such as ~S 1 V S 2 and an assignment of K 1 to S 1 and K 2 to S 2 one can evaluate the formula and place its outcome in one or the other of the classes. The assignment of K 1 to S 1 places ~S 1 in K 2, and now we can see that our assignment causes the formula to fall into class K 2. Thus by definition our formula is ...
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication[1][2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...
Ads
related to: contraposition of a statement examples in geometry classkutasoftware.com has been visited by 10K+ users in the past month