1.8 Proof Methods and Strategies

Question 1

Proof by cases

Answer 1

Proving by considering different cases
p1-> q
p2->q
p3->q
——–
p->q

Question 2

Constructive proof of existence

Answer 2

Proving ∃

Question 2

Constructive proof of existence

Answer 2

Proving ∃x by finding an element a (called the witness) such that P(a) is true

Question 3

Non-constructive proof

Answer 3

Not finding an element where P(a) is true
Example: Using proof by contradiction to show that the negation of ∃x implies a contradiction

Question 4

Uniqueness proof

Answer 4