00:01
In this problem we are asked to form the truth tables for the given statements.
00:11
In subpart a we are given p and s.
00:16
So the input is for p and s and the output which is y equals to p and s.
00:23
So here the values of the input for p are 0 -0 -1 -1 and the values of s are 0 -1 -0 -0 -0 -1.
00:31
So, y equals to p and s, that is p times s.
00:36
We have 0 times 0, 0 times 1, 0 times 0, 1 times 1 1 1.
00:44
So therefore, this is the required answer for subpart a.
00:50
In subpart b, we are provided with the statement, if not q, then s.
00:59
So here we have q which is 0 -0 -1 -1 and we have s which is 0 -1 -0 -1.
01:08
Not q implies the negation of q.
01:12
So 0 becomes 1, 0 becomes 1, 1 become 0, 1 become 0, 1 become 0.
01:18
If not q, then s.
01:21
So this gives us 0 only when the truth 1 becomes 0.
01:27
In all other places we have the value to be true.
01:31
So here we have 0 -1 -1 -1.
01:37
And this is the required answer for sub -part b.
01:43
In sub -part c we are provided with the statement, not p if and only if s.
01:53
So we have p whose values are 0 -0 -1 -1.
01:58
And not p, that is negation p is 1 .1 .00.
02:04
And the values of s are 0101.
02:08
So now we need to find out negation p if and only if s.
02:14
The values of this output are 0 when both the inputs are of the same value.
02:24
So here we have 1 and 0.
02:27
So the value of this would be 0.
02:30
Next we have 1 and 1, so the value of this is 1.
02:33
Next we have 0 and 0.
02:35
So the value of this is 1 since both are the same.
02:38
And lastly we have 0 and 1.
02:40
Since both the values are different, we get 0.
02:43
So this is the required answer for subpart c.
02:48
In subpart d, we are provided with the statement q or p and not s...