Ashwin_Mohan wrote:
There are only 2 values that the premise and conclusions can take. True and False. Thus the question states that
A valid argument is often defined as one in which it is not possible for all the premises to be true and the conclusion false
from this we can infer that if one of the premises is not true(= false) then the conclusion cannot be true (for a valid argument that is!!)
That is not a valid inference. While the question doesn't say that there are only two values the premise and conclusion can take, it doesn't make a difference if we assume this to be the case. An argument is
valid if:
If the premises are true, the conclusion is true.
The lone inference we can make from this is the contrapositive (from "If A then B" you can always conclude "If not B then not A"). That is, we can conclude:
If the conclusion is false, the premises are false (well, at least one of them is).
The inference you have made, "If the premises are false, the conclusion is false", is called the 'inverse'. That is, you've translated "If A then B" into "If not A then not B". This is not a legitimate inference to draw, as I will illustrate with an example. Suppose I'm standing next to a swimming pool, and have no shelter nearby. Then the following may be true:
"If it rains, I get wet."
We can certainly deduce the contrapositive:
"If I'm not wet, it's not raining."
We cannot conclude the inverse:
"If it's not raining, I'm not wet". I might be in the swimming pool.
Equivalently, we cannot deduce the converse (I say equivalently, because the converse is the contrapositive of the inverse- they're logically the same):
"If I'm wet, it's raining." Again, I might be swimming.