Question 1164740: Explain, without using a truth table, while the statement (p ∨ ¬q) ∧ (q ∨ ¬r) ∧ (r → ¬p)
is true when at least one of p,q,r is true, and at least one is false, and why the statement is false when p, q, r all have the same truth value.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Something is wrong with the wording here, because the words:
"true when at least one of p,q,r is true"
contradict the words:
"false when p, q, r all have the same truth value."
whenever p, q, r are all TRUE.
That's because when p, q, r are all true, then certainly at least one is
true, so the statement is TRUE.
However, also when p, q, r are all true, then they all have the same truth
value, so the statement is FALSE.
The statement can't be both TRUE and FALSE, so you need to ask your teacher
to correct the wording.
Edwin
|
|
|
