if I derive a false from p implies not q, can I conduct a p implies q?
Question
if I derive a false from p implies not q, can I conduct a p implies q?
Solution
No, you cannot.
If you derive a false from "p implies not q", it means that the implication "p implies not q" is not true. However, this does not automatically mean that "p implies q" is true.
In logic, "p implies not q" and "p implies q" are not necessarily opposites. The opposite of "p implies not q" would be "p and q", meaning that both p and not q cannot be true at the same time.
So, if you derive a false from "p implies not q", you can conclude that there is a situation where p is true and q is also true. But this does not mean that "p implies q" is always true. There could be situations where p is true and q is false.
Therefore, you cannot conduct a "p implies q" from deriving a false from "p implies not q".
Similar Questions
p → q is logically equivalent to
The contrapositive of p → q is the proposition of
p → q is logically equivalent to ¬p ∧ q¬p ∨ q¬p ∨ ¬qp ∨ ¬q
Given Similar as Valid InferenceIf p, Then q If ~q, Then ~pOnly If p, Then q If q, Then p If ~p, Then ~qUnless p, Then q If ~p, Then q If ~q, Then pEither p or q If ~p, Then q If ~q, Then p
The contrapositive of p → q is the proposition of ____________ans.q → p¬p → ¬q ¬q → p¬q → ¬p
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.