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I think i did this right but not sure! The directions are: Determine whether the statement is true or false. Prove the statement directly from the definitions or give a counter exmaple if it is false.

A sufficient condition for an integer to be divisble by 8 is hat it be divisble by 16.

[tex]\forall[/tex] integers n, if n is divisble by 8, then n is divisble by 16. This is a true statement.

Proof: Suppose n is an integer divisble by 8. BY definition of divisbility, n = 8k for some integer k. But, 8k = 4*2k, and 2k is an integer becuase k is. Hence n = 4*(some integer) and so n is divisble by 16.

Thanks!