00:01
Hello, let's have a look at the question.
00:02
So here it is given that using the truth table we have to determine the given proposition.
00:09
So for the a part we have been given the proposition as p symbol this q and then we have arrow sign to r then double arrows then we have p single arrow to negation of q and we have here r and we have to state whether this is a tautology or not.
00:38
So here first of all let us construct the truth table.
00:42
So here we will take 1 for true and 0 for false.
00:48
So first of all let us draw for p and q.
00:52
So here we will have 0 0 0 0 and then we have 1 1 1 1 then here we have 0 0 1 1 0 0 1 1 then we have here r and this will be 0 1 0 1 0 1 and 0 1.
01:12
So now we have p and q.
01:15
So this will be 0 0 this also 0 0 0 0 and this will be 1 and 1.
01:25
Next we have q or r.
01:29
So this will be 0 1 here also 1 then 1 and for q or r this is 0 then here we have 1 1 and 1 then here we have negation of q or r.
01:46
So this will be 1 0 0 0 then we have 1 0 0 and 0 then here we will take p and q to r.
02:00
So this will be 1 1 1 1 1 1 and this will be 0 and this is 1.
02:09
Finally we have p to negation of q or r.
02:14
So this will be 1 then this is also 1 1 1 1 and this is 0 0 and 0...