MATH135 Final: Math 135 Final Notes

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Wentang Kuo

Document Summary

Since a/b, a/c, there exists k1, k2 integers such that b=k1a, c=k2a. Since k1, k2, x, y are integers, k1x + k2y is also an integer. It finishes the proof. a|b a, b are integers a=divisor b=dividend. Types of proofs: direct proof [a=>b, contrapositive. Since k1, k2 are integers; k=k1. k2 are also integers. Disjunction: a or b both true one true + one false . Ex: if a, then b if a, then not b . A => b b => a a b. Two statements are logically equivalent if same truth tables. Ex: prove all n is a product of primes assume n is not a product of primes + it is the smallest one. Let a=8 and show that a does not follow the restriction. Composite: n>1 such that n is a product of. [k can be -2,-1,0,1,2 ][|k| can be 1,2,3 ] b=k. a => |b| = |k a| = |k|. |a| >= 1. |a| = |a|