[–] 1 point2 points ago

the first formula is saying that if A is true, then B and C are true only if the other is true. so if A is true and B and C are both false, the first formula is satisfied. the second formula is not satisfied with this arrangement

[–]phil. of law, metaethics, applied ethics 0 points1 point ago

To add on to the point, I offer the following explanation.

A bi-conditional is true if either all variables are true or all variables are false. As such the (B <-> C) portion is true if both are T or F. As long as B and C have the same truth value then the statement comes out true.
So long as A is also T, then regardless of whether B and C are both T or both F, then the whole statement comes out true.

This is not the case in the disjunctive.

[–][S] 3 points4 points ago

Thanks very much! I completely missed this and spent about 30 minutes staring into space confused. (1,0,0) satisfies the first formula and not the second!

[–] 0 points1 point ago

To simplify the language used here:

If A, then SAME.
If not-A, then DIFF.

SAME means B and C are the same: (T, T) or (F, F).
DIFF means B and C are different: (T, F) or (F, T).

[–] 0 points1 point ago

First, if a formula implies another tautologically, it can't be the case that the first is true while the second is false.

So, they are asking you to prove two things:

• That there are situations in which the first formula is true and the second one is false

• That there are situations in which the second formula is true and the first one is false

There are several ways to go on about this. The simplest way is to draw a truth table and find a line in which the first formula is true and the second is false, and another line in which the second formula is true while the first one is false.
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