00:01
In this question we need to tell that which of the following or the four options is a tautology.
00:07
So first of all what is the tautology is when the given expression is true in all the cases, then it is called a tautology.
00:20
So what we can do is we will check for all the expressions and check whether it is a tautology or not.
00:29
Now suppose we do for the first option.
00:34
It is negation p and p or q to q.
00:42
So we know that negation p and this is this can be reduced to negation of p or q like this.
00:56
So this expression is equal to negation p and negation p.
01:02
And negation q or q.
01:09
Now if we put this negation p inside this or also we can do is first of all do this or q inside that so it will give us as negation p or q and q or negation q so q or negation q will always be true as one of these will always happen so it is negation p and negation p or q so putting this negation p inside we can do it like negation p and negation p or negation p and q we can see that it does not simplify anything so we can take some of the cases for this to be always true suppose this is a pathology then then p should always be false.
02:21
So if p is always false, then we can say that this is always true.
02:27
So true and something...