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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  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,342 Thanks: 2465 Math Focus: Mainly analysis and algebra 
My translation would be: Quote:
 
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: 7,342 Thanks: 2465 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: 7,342 Thanks: 2465 Math Focus: Mainly analysis and algebra 
Sorry! I think they are being rather picky. I see all both as statements.

September 10th, 2014, 08:59 PM  #7 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88 
My natural inclination: $\forall s,t \in \Bbb Z: st \in 2\Bbb Z \implies (s \in 2\Bbb Z)\vee(t\in 2\Bbb Z)$ 
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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