Expert: Paul Klarreich - 11/6/2008

Question
Let a,b, and m be integers. Prove that if 2a+3b >or= 12m+1, then a >or= 3m+1 or b >or= 2m+1.

Answer
Questioner:   Pete
Category:  Calculus
Private:  No
 
Subject:  Proofs
Question:  Let a,b, and m be integers. Prove that if 2a+3b >= 12m+1, then a >= 3m+1 or b >= 2m+1.
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Some mathematical semantics. (Fancy words that refer to what sentences mean.)

If  (X or Y) is a false statement, then X and Y are both false statements.

Assume  a < 3m + 1  AND  b < 2m + 1

If a < 3m + 1, then a <= 3m, and  2a < 2(3m)

If  b < 2m + 1, then  b <= 2m, and  3b < 3(2m + 1)

Now put these together:

2a <= 2(3m)
3b <= 3(2m)
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and draw a conclusion.

Take it from there.