For Thursday\'s class, write one proof for each of the following statements whic

Question

For Thursday's class, write one proof for each of the following statements which is true.
1. For all integers m, if m > 2 then m^2 - 4 is composite.

These proofs will be collected and graded for the following elements:
Any proof must begin with Proof:" and end with a symbol (which may be lled in; personal
preference)
Proofs must consist of complete sentences, even with math symbols taking the place of some phrases:
+" is plus", =" is equals" or is equal to", etc.
Any equations must be displayed (new line, centered text). NOT in-line.
The rst sentence of a direct proof of a universal statement should always have the same format.
Use this format.
Proofs should end as soon as the nal conclusion is made.
Note: In no way is your grade dependent on the accuracy of your proof, or even on the accuracy of your
T/F decision for a statement. (However, you must show at least one proof)

Explanation / Answer

Proof :

This statement is false. A counter example is m=3.

      Although 3 > 2, 32 - 4= 5, which is not composite.

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