Proofs

Proof vs Show

Proof= Using LHS AND RHS (solve both simultaneously in order to prove that they are equal to eachother or not depends on question)

Show= LHS only or RHS only. Don’t use both.

Even =

Odd =

Prove by contradiction

Prove by contradiction

Prove by contradiction

Prove by contradiction

What is the contradition of this:

(…) is odd then n is even

(….) AND n are both odd because after is smt = statement (don’t change) and after then is assumption(that will be contradicted)

How to write inductions

Basis: plug in n=0,1,2 depends. Simple whole number

Induction: Assume true n=k and show true for n=k+1(add 1 in order to show it does work for other numebrs) and plug in k+1 to show that LHS is RHS

Write the format of induction

Show by induction

Show by induction part e

Prove by induction

Product/sum of two consecutive integers is always?

Product= even

Sum= Odd