Mathematical Reasoning and Induction
De Morgan's Laws of Logic
Expresses the negation of a disjunction or conjunction in terms of individual negations.
Distributive Laws of Logic
Distributes conjunction over disjunction and disjunction over conjunction.
Conditional as Disjunction
Rewrites a conditional statement into an equivalent disjunction.
Negation of Conditional Statement
A conditional is false precisely when the hypothesis is true and the conclusion is false.
Contrapositive Equivalence
A conditional implication is logically equivalent to its contrapositive.
Converse and Inverse
Defines the converse and inverse of an implication, which are contrapositives of each other.
Biconditional Statement
Decomposes a biconditional equivalence into two mutually reciprocal implications.
Principle of Mathematical Induction
Proves a proposition for all natural numbers by validating the base case and the induction step.