Chapter 5. Existence and Proof by Contradiction

Question 1

Proof by Contradiction

Answer 1

Question 2

Theorem 5.2.5. (The Fundamental Theorem of Arithmetic)

Answer 2

Question 3

Remark:

Let R be the quantified statement ∀x∈ S, P(x) ⇒ Q(x). Then the negation of R is:

Answer 3

Question 4

Proving an Existence Proof

Answer 4

Question 5

Proving Unique Existence Proofs:

Answer 5

Question 6

Theorem 5.4.6. (Intermediate Value Theorem)

Answer 6