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Does anyone understand this logic question?

 

01-19-14 12:32 PM
OracleofthePenguin is Offline
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Find the necessary condition on c such that ac = bc => a = b

I think it's the proposition (ac=bc) implies (a=b), but I have no clue what c is. It seems like it's its own condition, but I've never seen a condition attached to another condition like that before. I've never heard the phrase "necessary condition on x" before either and the internet isn't turning up any results...For context, we're just doing simple propositional logic. So... p=>q, q=>p is the converse, ~p=>~q is the inverse, here's a bunch of premises prove a conclusion is true, that sort of thing.
Find the necessary condition on c such that ac = bc => a = b

I think it's the proposition (ac=bc) implies (a=b), but I have no clue what c is. It seems like it's its own condition, but I've never seen a condition attached to another condition like that before. I've never heard the phrase "necessary condition on x" before either and the internet isn't turning up any results...For context, we're just doing simple propositional logic. So... p=>q, q=>p is the converse, ~p=>~q is the inverse, here's a bunch of premises prove a conclusion is true, that sort of thing.
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01-20-14 04:49 AM
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hmm select run* Haunter has successfully escaped*
hmm select run* Haunter has successfully escaped*
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01-20-14 07:47 AM
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Oooh proving~ fun times in Discrete math.
I might be able to help since I've already finished college Discrete Math, but I'll have to know what proving rules and techniques have already been tackled by your teacher (aside from the three you've listed)to serve as a clue for us to know "where" he/she wants the logic to go.

edit:

"Find the necessary condition on c..." just means "what values are possible for c to have that could make ac = bc => a = b possible?"
Oooh proving~ fun times in Discrete math.
I might be able to help since I've already finished college Discrete Math, but I'll have to know what proving rules and techniques have already been tackled by your teacher (aside from the three you've listed)to serve as a clue for us to know "where" he/she wants the logic to go.

edit:

"Find the necessary condition on c..." just means "what values are possible for c to have that could make ac = bc => a = b possible?"
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(edited by Juliet on 01-20-14 08:02 AM)    

01-20-14 08:15 AM
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I thought so. I decided to go with "c must be true." Thank you for the answer. :3
I thought so. I decided to go with "c must be true." Thank you for the answer. :3
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