How do we test the validity of the following
(~p^ q) , (p--> r) , (~r-->s) , (s-->t) :- t
5 answers
From 3 and 4 using law of syllogism , we can get~r-->t is true , but how do we test the validity of t only??
I don't think we can say anything about t
we know ~p but we have no information about ~p -> ??
we know ~p but we have no information about ~p -> ??
Since ~p^q is true can we take ~p is true and because of that ~p-->~r is true(inverse of 2)
And then using the law of syllogism repetedly, we get ~p--> t is true.
And finally using law of detachment can we get t is true(~p-->~t is true and ~p is true)?
And then using the law of syllogism repetedly, we get ~p--> t is true.
And finally using law of detachment can we get t is true(~p-->~t is true and ~p is true)?
~p--> t is true*
I don't like it.
p -> r
does not mean that ~p -> ~r
The converse is not always true.
All we know is that ~r -> ~p
From #1, we know that ~p is true, but we know nothing about what happens for ~p
p -> r
does not mean that ~p -> ~r
The converse is not always true.
All we know is that ~r -> ~p
From #1, we know that ~p is true, but we know nothing about what happens for ~p