Methods of Proof

Proving a statement using a logical method of rules of inference is often called?

• formal proof

• informal proof

• alternative proof

• mathematical proof

Show that there is a specific value of x for which the statement is true.

• constructive existential proof

• non-constructive existential proof

• counterexample proof

• direct proof

• exhaustion proof

Show that a value of x exists, but do not actually find it.

• constructive existential proof

• non-constructive existential proof

• counterexample proof

• direct proof

• exhaustion proof

Find a single example that is not true in order to disprove it.

• constructive existential proof

• non-constructive existential proof

• counterexample proof

• direct proof

• exhaustion proof

Assume the hypothesis is true then show that the conclusion is also true.

• constructive existential proof

• non-constructive existential proof

• counterexample proof

• direct proof

• exhaustion proof

Check for all possible values of n to see if the statement is true.

• constructive existential proof

• non-constructive existential proof

• counterexample proof

• direct proof

• exhaustion proof

Which mathematical definition has the following properties?

n = 2k + 1 where k is an integer

• odd and even number

• divisibility

• rational number

• Quotient-remainder theorem

• Floor and ceiling

Which mathematical definition has the following properties?

A unique integer n such that n <= x < n

• odd and even number

• divisibility

• rational number

• Quotient-remainder theorem

• Floor and ceiling

Which mathematical definition has the following properties?

There exist a unique integer q and r such that

n = dq + r and 0 <= r < d

• odd and even number

• divisibility

• rational number

• Quotient-remainder theorem

• Floor and ceiling

Which mathematical definition has the following properties?

a Real number can be expressed as a quotient of two integers with a nonzero denominator.

• odd and even number

• divisibility

• rational number

• Quotient-remainder theorem

• Floor and ceiling