proof_primer_flashcards
What is a statement in logic?
A statement (or proposition) is a sentence that is either true (T) or false (F).
What is the negation (~ or ¬) of a statement S?
The opposite of S; if S is true, ¬S is false, and vice versa.
What is a conjunction (AND, ∧)?
A statement that is true only if both parts are true.
What is a disjunction (OR, ∨)?
A statement that is true if at least one part is true.
What is a conditional statement (implication, →)?
If A, then B. It is false only when A is true and B is false.
What is a biconditional statement (↔)?
A is true if and only if B is true.
What is a direct proof?
A proof where you assume the hypothesis is true and logically deduce the conclusion.
What is proof by contrapositive?
Instead of proving ‘If A, then B,’ you prove ‘If not B, then not A.’
What is proof by contradiction?
Assume the opposite of what you want to prove and show this leads to a contradiction.
What is proof by exhaustion?
Checking all possible cases individually (useful for small, finite cases).
What is proof by induction?
A proof method used for statements about natural numbers using a base case and an inductive step.
What is the converse of ‘If A then B’?
If B then A. (Not always true.)
What is the contrapositive of ‘If A then B’?
If not B then not A. (Always logically equivalent to the original statement.)
What is an example of a direct proof?
If x is even, then x² is even. Assume x = 2k, then x² = 4k², which is even.
What is an example of proof by contradiction?
Assume √2 is rational, then show it leads to a contradiction. Hence, √2 is irrational.
