Chapter 2 vocab Flashcards
Inductive reasoning
reasoning based on the patterns you observe
Conjecture
conclusion you reach using inductive reasoning
Counterexample
example that shows that a conjuncture incorrect
Hypothesis
the part “p” following if
Conditional
an if-then statement, p->q
Conclusion
the part “q” following then
Truth Value
of a conditional is either true or false
Negation
of a statement “p” is the opposite of the statement, ~p
Converse
exchange the hypothesis and the conclusion, q->p
Inverse
negate both the hypothesis and the conclusion of the conditional, ~p->~q
Contrapositive
negate both the hypothesis and the conclusion of the converse, ~q->~p
Equivalent statements
have the same truth value
Biconditional
single true statement that combines a true conditional and its true converse, join using if and only if, iff, p<->q
Deductive Reasoning
process of reasoning logically from given statements or facts to a conclusion
Law of Detachment
If the hypothesis of a true conditional is true, then the conclusion is true
Law of Syllogism
allows you to state a conclusion from two conditional statements when the conclusion of one statement is the hypothesis of the other statement
Proof
convincing argument that uses deductive reasoning, logically shows why a conjecture is true
Two Column Proof
lists each statement on the left and the justification(reason) is on the right; each statement must follow logically from the steps before it
Properties of Equality
Addition property
Subtraction Property
Multiplication Property
Reflexive Property
Symmetric Property
Transitive Property
Distributive Property
Symmetric Property
x=2y the 2y=x
Reflexive Property
a=a
Transitive Property
x=y
Theorem
conjecture or statement that you can prove
Paragraph proof
written as sentences in a paragraph
