Question

how do you prove premises are inconsistent?

Answer 1

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

Answer 2

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?

Answer 3

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

Answer 4

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