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Discrete structures - logic problem

 

Discrete structures - logic problem

swimchelle

25 May, 2009 - 12:31 AM
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Hi I have just started learning discrete structures, propositional and predicate logic
I have no idea where to start on this problem.
Prove (b(1)=J ^ b(2)=S ^ b(3)=C) v (b(1) = S ^ b(2)=C ^ b(3)=J) and then
(b(3)=J -> b(1)=S ^ b(2)=C) ^ (b(3)=C -> b(1)=J ^ b(2)=S)
Any hints on where to start would be much appreciated!!
THANKS

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IngeniousHax

RE: Discrete Structures - Logic Problem

25 May, 2009 - 09:48 AM
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Do you have values for b? or is that all the information you have?
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Dantheman

RE: Discrete Structures - Logic Problem

28 May, 2009 - 03:28 PM
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QUOTE(swimchelle @ 25 May, 2009 - 12:31 AM) *

Hi I have just started learning discrete structures, propositional and predicate logic
I have no idea where to start on this problem.
Prove (b(1)=J ^ b(2)=S ^ b(3)=C) v (b(1) = S ^ b(2)=C ^ b(3)=J) and then
(b(3)=J -> b(1)=S ^ b(2)=C) ^ (b(3)=C -> b(1)=J ^ b(2)=S)
Any hints on where to start would be much appreciated!!
THANKS


I have a good understanding of propositional logic (studied it in Discrete Math, Mathematical Logic, and Logic classes), but I have no idea what you wrote. I understand that

^ is a conjunction
v is a disjunction
-> is implication
= is equivalence

but everything else makes absolutely no sense. For example what is b(2) supposed to mean?
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JayFCox

RE: Discrete Structures - Logic Problem

31 May, 2009 - 10:42 AM
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QUOTE(Dantheman @ 28 May, 2009 - 03:28 PM) *

QUOTE(swimchelle @ 25 May, 2009 - 12:31 AM) *

Hi I have just started learning discrete structures, propositional and predicate logic
I have no idea where to start on this problem.
Prove (b(1)=J ^ b(2)=S ^ b(3)=C) v (b(1) = S ^ b(2)=C ^ b(3)=J) and then
(b(3)=J -> b(1)=S ^ b(2)=C) ^ (b(3)=C -> b(1)=J ^ b(2)=S)
Any hints on where to start would be much appreciated!!
THANKS


I have a good understanding of propositional logic (studied it in Discrete Math, Mathematical Logic, and Logic classes), but I have no idea what you wrote. I understand that

^ is a conjunction
v is a disjunction
-> is implication
= is equivalence

but everything else makes absolutely no sense. For example what is b(2) supposed to mean?


I think he's slightly misunderstanding the problem.
b(2) doesn't mean anything more than what's stated. b2 either is equal to S or C!
Just take
(b(1)=J ^ b(2)=S ^ b(3)=C) v (b(1) = S ^ b(2)=C ^ b(3)=J)
as "the truth".

So, Either
b(1) is J and b(2) is S and b(3) isC
or
b(1) is S and b(2) is C and b(3) is J

From that, prove
1. if b(1) is J then b(2) is S and b(3) is C
and
2. if b(2) is S then b(2) is C and b(3) is J

Hope this helps,

Jay
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Dantheman

RE: Discrete Structures - Logic Problem

6 Jun, 2009 - 07:58 AM
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Oh. Well, in that case I can't see what can be the problem. The question basically gives the answer right away.

Look at the value of b3, then look if it matches any given conditions. Can't get any simpler than that.
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