M3

Question 1

we need this to determine whether a
mathematical argument is correct or incorrect and
construct mathematical arguments.

Answer 1

mathematical reasoning

Question 2

is not only important for
conducting proofs and program verification, but also for
artificial intelligence systems (drawing inferences)

Answer 2

Mathematical reasoning

Question 3

is a basic assumption about mathematical

structures that needs no proof.

Answer 3

axiom

Question 4

used to demonstrate that a particular

statement is true.

Answer 4

proof

Question 5

A proof consists of a sequence of
statements that form an argument.
The steps that connect the statements in such a
sequence are the X

Answer 5

rules of inference

Question 6

Cases of incorrect reasoning are called X

Answer 6

fallacies.

Question 7

is a statement that can be shown to be

true

Answer 7

theorem

Question 8

is a simple theorem used as an intermediate

result in the proof of another theorem.

Answer 8

lemma

Question 9

is a proposition that follows directly from

a theorem that has been proven.

Answer 9

corollary

Question 10

is a statement whose truth value is

unknown. Once it is proven, it becomes a theorem.

Answer 10

conjecture

Question 11

provide the justification of the

steps used in a proof.

Answer 11

Rules of inference

Question 12

just like a rule of inference, an X consists of

one or more hypotheses and a conclusion.

Answer 12

argument

Question 13

We say that an argument is X, if whenever all its

hypotheses are true, its conclusion is also true.

Answer 13

valid

Question 14

The principle of X is a useful tool for
proving that a certain predicate is true for all natural
numbers.

Answer 14

mathematical induction

Question 15

It cannot be used to discover theorems, but only to prove

them

Answer 15

mathematical induction