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how do you prove premises are inconsistent?

Mathematics
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Set one of them as false. If you can FORCE the rest of the premises to be TRUE, then your premised are not consistent. Say B is False instead of True. not(B&C) {C could be True or False and the premise could be made True. not forced!} A or (B and C) {A is forced True since B makes (B&C) False} A-> C {C is forced True because A is True} not(B&C) {C could be True or False and the premise could be made True. not forced! But C was already shown to be True, so statement holds as true.} Not Consistent
so, if you had the premises 1) (b implies c) implies A 2) b implies D 3) D implies c 4) not a or not d how would you do that?
i did proof by exhaustion :) i tried every combo to make 4 true; and came up with at least one other premise false; so in the end, none of it was good

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1) ( b ^ -c) v a 2) -b v d 3) -d v c 4) -a v -d i wonder if these equivalence statements would have made life easier

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