2: Reasoning and Proof Flashcards
reasoning based on patterns you observe
inductive reasoning
a conclusion you reach using inductive reasoning
conjecture
an example that shows that a conjecture in incorrect
counterexample
an if-then statement
conditional
the part “p” following “if”
hypothesis
the part “q” following “then”
conclusion
the _________ of a conditional is either true or false
truth value
the _________ of a statement “p” is the opposite of the statement
negation
_________________ have the same truth value
equivalent statements
exchange the hypothesis and the conclusion
converse
negate both the hypothesis and the conclusion of the conditional
inverse
negate both the hypothesis and the conclusion of the converse
contrapositive
connect two or more statements with “and”
conjunction
connect two or more statements with “or”
disjunction
a single true statement that combines a true conditional and its true converse
biconditional
(sometimes called logical reasoning) the process of reasoning logically from given statements or facts to a conclusion
deductive reasoning
If the hypothesis of a true conditional is true, then the conclusion is true
if p → q is true
and p is true
the q is true
Law of Detachment
a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement
if p → q is true
and q → r is true
then p → r is true
Law of Syllogism
a = a
reflexive property
if a = b, then b = a
symmetric property
if a = b and b = c, then a = c
transitive property
a convincing argument that uses deductive reasoning
proof
Lists each statement on the left. The reason for each statement is on the right.
two-column proof
a conjecture or statement that you prove true
theorem
proof written as sentences in a paragraph
paragraph proof
