00:01
Let's have a look at the question.
00:03
So the question state construct a truth table for the following statement form.
00:08
So we have p implies that q implies r and then we have if and only if here we have p and q together imply.
00:33
So here we have to construct a truth table for this statement.
00:36
So here we will have a table for p q and r.
00:41
Let us draw a line here and here we have for q for r then we have for representing p and q together.
00:52
Then we have for q implies r.
00:55
Next we will have for p implies q which implies r.
01:01
Then next we have p and q together they imply r and then we have for whole p implies q implies r and this whole implies if and only if we have p and q which together implies to r.
01:25
Now here we will take the first case here false false false false.
01:31
Then here we have true true true and true.
01:35
Next we will have false false then true true false false and true true.
01:43
Next we will have false true false true false true false and true.
01:50
So these are the entries for p q and r.
01:54
Now p and q in false and false will be false then again here false and false will give us false.
02:02
Then we have false and true will give us false again false and true will give false.
02:09
Then true and false also gives us false then true and false again gives false.
02:14
Now here we have true and true will give us true and at last true and true again will give true.
02:20
Now let us construct here also lines to make this table clear.
02:26
Now q implies r.
02:28
Here q implies r will give false and false.
02:32
So this statement is true that if q is false then r is false.
02:37
Then if q is false we have r is true.
02:40
So the statement is also true.
02:43
Then here we will get false...