Chapter 2: Proofs

Question 1

Even Integer Expression

Answer 1

x = 2k

Question 2

Odd Integer Expression

Answer 2

x = 2k + 1

Question 3

Parity

Answer 3

The parity of a number is whether it is even or odd

Question 4

Rational Number

Answer 4

A number is rational if:
–y does not equal 0
–r = x/y

Question 5

Prime Number

Answer 5

–Only if n >1
–Can only be divided by and 1 and itself

Question 6

Composite Number

Answer 6

–Only if n >1
–Can be divided by more than 1 and itself

Question 7

Theorem

Answer 7

A statement that can be proven to be true

Question 8

Proof

Answer 8

Consists of a series of steps, each of which follows logically from assumptions, or from previously proven statements

Question 9

Axioms

Answer 9

Statements assumed to be true

Question 10

Consecutive Intergers

Answer 10

Two integers are consecutive if one of the number is equal to 1 plus the other number

Question 11

Counterexample

Answer 11

An assignment of values to variables that shows that a universals statement is false

Question 12

Existence Proof

Answer 12

A proof that shows that an existential stmt is true

Question 13

Constructive Proof of Existence

Answer 13

Gives a specific example of an element in the domain or a set of directions to construct an element in the domain that has required properties

Question 14

Existential Instantiation

Answer 14

A law of logic that says if an object is known to exist, that that object can be given a name, as long as the name is not currently in use to denote something else.