## a123 4 years ago how do you prove premises are inconsistent?

1. MissMathmatics

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

2. a123

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?

3. amistre64

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

4. amistre64

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