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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