MATH135 Lecture Notes - Lecture 22: Contraposition, Vise, Counterexample

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Shane Bauman

Document Summary

Implications: look at the conclusions (except the f f case) Aussume a to be true and then show that this leads to. Negation: if the statement is correct then its negation would be false (vise versa) if the statement is false then its negation would be corret. Contrapositive: (instead of proving its implication is correct we can use contra positive) Tip if the negation conculstion gives more info then origina; hypothesis, then it"ll be better to use the contrapositive a => b then b => a. Contradiction assume a is true then contradict it. More complcated implications: (a^b) => c same (avb) => c (a=>c) ^ (b=>c) a=>(b^c) (a=>b) ^ (a=>c) a=>(bvc) (a^ b) => c. Bbd: if a|b and b 0, then |a| |b|, a b or b=0. Example: a= {a/b : a,c (cid:1488) z and b 0 } Set difference: s-t= {x: x(cid:1488)s x(cid:1489)t} compliment s: x(cid:1489)s.