Chapter 2 vocab

Question 1

Inductive reasoning

Answer 1

reasoning based on the patterns you observe

Question 2

Conjecture

Answer 2

conclusion you reach using inductive reasoning

Question 3

Counterexample

Answer 3

example that shows that a conjuncture incorrect

Question 4

Hypothesis

Answer 4

the part “p” following if

Question 4

Conditional

Answer 4

an if-then statement, p->q

Question 5

Conclusion

Answer 5

the part “q” following then

Question 6

Truth Value

Answer 6

of a conditional is either true or false

Question 7

Negation

Answer 7

of a statement “p” is the opposite of the statement, ~p

Question 8

Converse

Answer 8

exchange the hypothesis and the conclusion, q->p

Question 9

Inverse

Answer 9

negate both the hypothesis and the conclusion of the conditional, ~p->~q

Question 10

Contrapositive

Answer 10

negate both the hypothesis and the conclusion of the converse, ~q->~p

Question 11

Equivalent statements

Answer 11

have the same truth value

Question 12

Biconditional

Answer 12

single true statement that combines a true conditional and its true converse, join using if and only if, iff, p<->q

Question 13

Deductive Reasoning

Answer 13

process of reasoning logically from given statements or facts to a conclusion

Question 14

Law of Detachment

Answer 14

If the hypothesis of a true conditional is true, then the conclusion is true

Question 15

Law of Syllogism

Answer 15

allows you to state a conclusion from two conditional statements when the conclusion of one statement is the hypothesis of the other statement

Question 16

Proof

Answer 16

convincing argument that uses deductive reasoning, logically shows why a conjecture is true

Question 17

Two Column Proof

Answer 17

lists each statement on the left and the justification(reason) is on the right; each statement must follow logically from the steps before it

Question 18

Properties of Equality

Answer 18

Addition property
Subtraction Property
Multiplication Property
Reflexive Property
Symmetric Property
Transitive Property
Distributive Property

Question 19

Symmetric Property

Answer 19

x=2y the 2y=x

Question 19

Reflexive Property

Answer 19

a=a

Question 20

Transitive Property

Answer 20

x=y

Question 21

Theorem

Answer 21

conjecture or statement that you can prove

Question 22

Paragraph proof

Answer 22

written as sentences in a paragraph