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 September 5th, 2014, 02:40 PM #1 Senior Member   Joined: Dec 2013 Posts: 137 Thanks: 4 Translating If - Then statements I have one that is throwing me. "If S and T are integers, such that s * t is an even integer, then S or T is an even integer." I am instructed to TRANSLATE not NEGATE the above sentence into an equivalent statement involving the universal quantifier ”For Any" the "such that" part of the statement is mixing me up. I want to say, "For any integers S and T, having an even integer as their product, Then S or T must be an even integer." But that doesn't sound right so I am pretty sure then it is not. Please help someone Last edited by greg1313; September 5th, 2014 at 03:05 PM.
September 5th, 2014, 03:31 PM   #2
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My translation would be:
Quote:
 For any (pair of) integers S and T to have an even product, either S or T must be even.

 September 5th, 2014, 03:50 PM #3 Senior Member   Joined: Dec 2013 Posts: 137 Thanks: 4 reply I actually was trying to write down pair (for it felt correct and I think I read over it) but I could not locate it in the online text around the problem. I will let you know V8 about any/all feedback I get back on this one particular question/problem. Also, ... what would I do without u V8? You have been here like clockwork all the time so thank you.
 September 5th, 2014, 04:39 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,308 Thanks: 2443 Math Focus: Mainly analysis and algebra The "pair of" is optional. The main differences between your version and mine were "having"/"to have" and the omission of "then".
 September 9th, 2014, 04:10 PM #5 Senior Member   Joined: Dec 2013 Posts: 137 Thanks: 4 Well the instructor said the following ...so not sure if I worded my post wrong or what but here is what was said. I submitted the following: Gyazo - 6db36b441cf66e77e847c8841cf2490a.png Instructor sent back the following: (0 pt) We are looking for direct traslation, not an interpretation. ”For any integers s and t such that s · t is an even integer, s or t is an even integer."
 September 9th, 2014, 04:55 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,308 Thanks: 2443 Math Focus: Mainly analysis and algebra Sorry! I think they are being rather picky. I see all both as statements. Thanks from mr. jenkins
 September 10th, 2014, 08:59 PM #7 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 My natural inclination: $\forall s,t \in \Bbb Z: st \in 2\Bbb Z \implies (s \in 2\Bbb Z)\vee(t\in 2\Bbb Z)$ Thanks from mr. jenkins and aurel5
 September 13th, 2014, 05:45 PM #8 Senior Member   Joined: Dec 2013 Posts: 137 Thanks: 4 @Deveno, You are dead on with that symbolic math language brother. I like your style. as a new AA student I'm of course just getting acclimated to symbolic language so when I read your feedback next to the question it's perfect. I'm reading like For any s and t that are integers such that s times t is even integers so s is even integer or t is even integer. not sure if thats quite translated right but I can follow the language Thank You Deveno and thank you V8 for being present on this site. This site has been such a comforter

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