- #1

Eclair_de_XII

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- 91

## Homework Statement

"Given: ##a,b,c∈ℤ##,

Prove: If ##2a+3b≥12m+1##, then ##a≥3m+1## or ##b≥2m+1##."

## Homework Equations

##P:a≥3m+1##

##Q:b≥2m+1##

##R:2a+3b≥12m+1##

## The Attempt at a Solution

Goal: ##~(P∨Q)≅(~P)∧(~Q)⇒~R##

Assume that ##a<3m+1## and ##b<2m+1##. Then ##2a+3b<2(3m+1)+3(2m+1)=12m+5##. But this doesn't necessarily imply that ##2a+3b>12m+1##. Can someone help me connect the dots?