October 7, 2004

Returned exams and went over them

Reviewed using contrapositive as a method of proof

Want to prove A → B

B → A is the converse (may be true but can’t be used to prove A → B is true)

B’ →A’ is the contrapositive (if it’s true then A → B is true)

If you need to prove that A is true if and only if B is true

then you need to prove A → B and B→ A

iff is the abbreviation for if and only if

In class we did: xy is odd iff x is odd and y is odd

Contradiction method is an indirect proof method.

The wff A Ù A’ is always false (represented by 0)

Can prove that P → Q by showing that P Ù Q → 0

(using the hypothesis and the negation of the conclusion)

In class we did: if n + n = n then n = 0

if √2 is rational then √2 = p/q

We talked about the serendipity section and went through

the 2 book examples.

We went over the principle of mathematical induction

Method:

prove P(1) is true

assume that P(k) is true for all k

prove that P(k+1) is true

If P(1) is true and (∀k) P(k) → P(k+1)

then P(n) is true for all positive integers n.

We went over Examples 14 and 15

Did them slightly differently than the book did

Homework assignment is up.