Introduction to Proofs Flashcards
Conjecture
A conclusion reached by using inductive reasoning.
Similar to a prediction.
Counterexample
A statement that proves a conjucture false.
Inductive Reasoning
Reasoning that reaches conclusion based on a pattern of spectific examples or past events. (Specific to General)
Deductive Reasoning
Reasoning logically from given facts to a conclusion.
(General to Specific)
Hypothesis
In an if-then statement, the hypothesis is the part that follows the if.
Conclusion
In an if-then statement, the conclusion is the part that follows the then.
Conditional Statement
A conditional statement in hypothesis (if) and conclusion (then) format.
Inverse
The inverse of the conditional statement.
“if not p, then not q.”
(Negative of hypothesis and conclusion)
Converse
The converse of the conditional statement .
“if q , then p.”
(Reverse the hypothesis and conclusion.)
Contrapositive
The inverse of the conditional statement.
“if not q, then not p.”
(Negative and reverses hypothesis and conclusion)
Two Column Proof
A convincing argument is the form of a Given (if) and Proof (then) followed by statements and reasons aligned in columns.
Paragraph Proof
A convincing argument with the statements and reasons written in connected sentences.
Flow Chart Proof
A convincing argument is the form of a Given (if) and Proof (then) followed by statements and reasons in connected boxes in logical order.
