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Flashcards in Proofs Deck (12)
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1

theorem

statement that can be proven to be true

2

proof

a series of steps, each of which follows logically from assumptions

3

axioms

statements assumed to be true

4

proof by exhaustion

prove the statement by checking each element individually

5

counterexample (chapter 4)

an assignment of values to variables that shows that a universal statement is false

6

direct proof

hypothesis p is assumed to be true and the conclusion c is proven as a direct result of the assumption

7

proof by contrapositive

proves conditional theorem of the form p → c by showing that the contrapositive ¬c → ¬p is true

8

even integer

2k

9

odd integer

2k+1

10

proof by contradiction

assume the theorem is false and then show that some logical inconsistency arises as a result of this assumption, also known as indirect proof

11

proof by cases

∀x P(x) breaks the domain for the variable x into different classes and gives a different proof for each class

12

set identity

an equation involving sets that is true regardless of the contents of the sets in the expression