Proofs

Question 1

Proposition

Answer 1

statement with premise and conclusion

p -> q

Question 2

Converse of a proposition

Answer 2

q -> p

proposition: if its snowing outside, then its cold outside
converse: if its cold outside, then its snowing outseide

Question 3

Inverse of a proposition

Answer 3

not p -> not q

proposition: if its snowing outside, then its cold outside
inverse: if its not snowing outside, then its no cold outside

Question 4

Contrapositive of a proposition

Answer 4

not q -> not p

proposition: if its snowing outside, then its cold outside
contrapositive: if its not cold outside, then its not snowing outside

Question 5

The original proposition and the contrapositve……..
and
The converse and the inverse……….

Answer 5

ALWAYS have the same truth value

Question 6

Methods of proof

Answer 6

1. ) direct proof:
   
   • prove p -> q
2. ) indirect proof:
   
   • prove not q -> not p
3. ) cases:
   
   • prove hypothesis p is equivalent P1 or P2 or…Pn
   • prove P1 -> q or P2 -> q or…..Pn->q
4. ) contradiction:
   
   • prove not q -> something ridiculous
5. ) induction