2: Reasoning and Proof

Question 1

reasoning based on patterns you observe

Answer 1

inductive reasoning

Question 2

a conclusion you reach using inductive reasoning

Answer 2

conjecture

Question 3

an example that shows that a conjecture in incorrect

Answer 3

counterexample

Question 4

an if-then statement

Answer 4

conditional

Question 5

the part “p” following “if”

Answer 5

hypothesis

Question 6

the part “q” following “then”

Answer 6

conclusion

Question 7

the _________ of a conditional is either true or false

Answer 7

truth value

Question 8

the _________ of a statement “p” is the opposite of the statement

Answer 8

negation

Question 9

_________________ have the same truth value

Answer 9

equivalent statements

Question 10

exchange the hypothesis and the conclusion

Answer 10

converse

Question 11

negate both the hypothesis and the conclusion of the conditional

Answer 11

inverse

Question 12

negate both the hypothesis and the conclusion of the converse

Answer 12

contrapositive

Question 13

connect two or more statements with “and”

Answer 13

conjunction

Question 14

connect two or more statements with “or”

Answer 14

disjunction

Question 15

a single true statement that combines a true conditional and its true converse

Answer 15

biconditional

Question 16

(sometimes called logical reasoning) the process of reasoning logically from given statements or facts to a conclusion

Answer 16

deductive reasoning

Question 17

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

Answer 17

Law of Detachment

Question 18

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

Answer 18

Law of Syllogism

Question 19

a = a

Answer 19

reflexive property

Question 20

if a = b, then b = a

Answer 20

symmetric property

Question 21

if a = b and b = c, then a = c

Answer 21

transitive property

Question 22

a convincing argument that uses deductive reasoning

Answer 22

proof

Question 23

Lists each statement on the left. The reason for each statement is on the right.

Answer 23

two-column proof

Question 24

a conjecture or statement that you prove true

Answer 24

theorem

Question 25

proof written as sentences in a paragraph

Answer 25

paragraph proof