Quiz 3

Question 1

a sentence describing a new term using already known terms

Answer 1

Definition

Question 2

a declarative sentence that is true or false, but not both

Answer 2

Proposition

Question 3

a proposition that was proved to be true

Answer 3

Theorem

Question 4

a sequence of sentences used to demonstrate that a statement is true. It uses axioms, definitions, already proven theorems, logical thinking, and creativity.

Answer 4

Proof

Question 5

a smaller theorem used to prove a bigger theorem (parent)

Answer 5

Lemma

Question 6

a smaller theorem that can be easily derived from a bigger theorem (child)

Answer 6

Corollary

Question 7

a claim. It becomes a theorem once it is proven.

Answer 7

Conjecture

Question 8

An integer n is ________ iff ∃k ε Z s.t. n = 2k.

Answer 8

even

Question 9

An integer n is ________ iff ∃k ε Z s.t. n = 2k + 1.

Answer 9

odd

Question 10

A set A is _______________ under operation multiplication (*) iff ∀a,b ε A s.t. a * b ε A.

Answer 10

closed (i.e. has closure)

Question 11

An integer n is ________ iff n > 1 and it has no positive divisor other than 1 and itself.
i.e. iff n > 1 and ∀r,s ε Z+ if n = r * s then r = 1 or s = 1.

Answer 11

prime

Question 12

An integer is __________ iff n > 1 and n is not prime.
i.e. iff n > 1 and ∃r,s ε Z+ s.t. n = r * s but r ≠ 1 and s ≠ 1.

Answer 12

composite

Question 13

r ε R is called a _____________ iff ∀a,b ε Z s.t. r = a/b and b ≠ 0.

Answer 13

rational number

Question 14

A real number is called a ________________ iff it is not a rational number.

Answer 14

irrational number

Question 15

Any integer n s.t. n > 1 is either a prime or it can be uniquely written as a product of primes in a non-decreasing order.

Answer 15

The Fundamental Theorem of Arithmetic (FTA)

Question 16

∀n ε Z ∀d ε Z s.t d ≠ 0 ______________, denoted d | n iff ∃k ε Z s.t. n = dk.

Answer 16

d divides n