If I am given 4 sentences:
a) ...
b) ...
c) ...
d) ...
and a conclusion
f) ...
How can I show that f) is not a logical consequence of a), b), c) and d) ?
One way: assume the premises are true, the conclusion is false, and you don't get a contradiction. This is rather difficult to apply, however, since how do you know if have done enough work to show there is no contradiction? Still, it is valid, if you can achieve it.