Advertisement
Lawnknome

Untitled

Jan 28th, 2015
250
0
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 0.44 KB | None | 0 0
  1. Use a proof by contraposition to show that If m2 + n2 is an odd integer, then m is odd or n is odd.
  2. Let p be “if m2 + n2 is an odd integer” and q be “m is odd or n is odd”.
  3. Contrapositive is “If neither m is odd nor n is odd, then m2 + n2 is not odd”
  4. Which is the same as “If m and n are even, m2 + n2 is even”
  5. m2 + n2 = 2km2 + 2kn2 definition of an even number
  6. = 2(km2 + kn2) Factor out a 2
  7. = 2(k’) k’ = km2 + kn2
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement