0:00
Hi.
00:01
In this question, we have two propositional variables, p and q, and we have some propositional formulas, and we want to select which of them are tautologies.
00:13
So a tautology is a statement that is true regardless of the truth values of the propositional variables.
00:21
So whether p and q are true or false, the formula will always be true.
00:25
So let's just go one by one.
00:28
First we have not p or not q and p or q.
00:40
So think about, you can kind of think reason about it like intuitively.
00:46
So is it always true no matter what the truth values of p and q are, that this will be true.
00:52
And because we have an and statement, both of these have to always be true.
00:59
But if p and q are both false then this statement will be true and this state won't be false and therefore the whole statement will be false so to reiterate if p and q are both are both false then this statement will be false so this one is not a tautology next we have p and p implies q implies q so first what it's saying, if we look at the hypothesis of this statement, which is p and p implies q.
01:42
So let's say again what this is saying.
01:45
It's saying if p is true and if p implies q, then q is true...