00:01
Okay, so we want to know if any of these compound propositions are satisfiable.
00:05
That is, if there is a truth, a combination of truth values that makes this compound proposition true.
00:17
For a, for a, we have p or q or not r and p or not q or or not s and p or not q or not s and not p or not q or not s and p or not q or not s and or q or not s well we have t in one two three four we have p and four sets of these disjunctions so let's set p true now we have not p right here so which is false but if we said q to be true i mean if we said q to be false we can make this true because we would have not p or not q and not q is true since q is false and we get that this entire thing is true regardless of the truth value of s therefore a is now we have b.
01:41
We have not p or not q or r not p or q or not s p or not q or not s p or not p or not r and p or not r and p or not s well again we can assign a truth value for not p since we have it in these three sets of disjunctions, we can set p is false, so not p is true.
02:18
So we have one, two, three of these are true.
02:21
And then for the rest, we have p is false.
02:26
So we must assign values to q and s.
02:31
Well, we have not as right here in this disjunction, and we have not as in this disjunction.
02:38
So if we set s to false, we will get that not s is true, making these two disjunctions with not s be true...