00:01
In this problem we are given that p, q and r are prepositional variables.
00:10
We are asked to determine whether p implies q implies r yields p implies r.
00:27
Now this symbol here is the turnstile simple and the preposition to the term style simple and the preposition to the the left of the simple is known as the premise and the proposition to the right of the simple is the conclusion now this statement is valid if and only if it is impossible for the premises to be true and the conclusion to be false.
01:14
So if we can prove that whenever the premises are true, the conclusions are true, then we can say this is a valid statement, otherwise it is not.
01:25
Now to check the validity, construct the truth tables with pqr, p implies q, p implies q, p implies q, and p implies r.
01:45
Now consider the first case when all the variables pq and r are true, then p implies q is true, p implies q is true and p implies r is also true.
02:00
Secondly, consider the case when p is false, q is true and r is true.
02:06
In that case, p implies q is true.
02:09
P implies q is true.
02:09
P implies q is true.
02:11
P implies q is true.
02:12
R is true and p implies r is also true.
02:17
Next consider the case when p is true, q is false and r is true.
02:24
Then p implies q is false.
02:28
P implies q is false...