Answer:
a
[tex]a \to b[/tex]
[tex]\neg b[/tex]
[tex]\neg a[/tex]
b
If all prime numbers are odd, then 2 is odd.
2 is not odd.
Therefore, it is not the case that all prime numbers are odd.
Step-by-step explanation:
Considering part A
The first sentence is
If all computer programs contain errors, then this program contains an error.
The second sentence is
This program does not contain an error.
The third sentence is
Therefore, it is not the case that all computer programs contain errors.
Now we will use a and b as the letter to denote the component sentences and [tex]\neg a[/tex] and [tex]\neg b[/tex] when the component sentences is not the case
So a = If all computer programs contain errors
and
b = this program contains an error.
Generally then is represented as [tex]\to[/tex]
Hence the first sentence is denoted as
[tex]a \to b[/tex]
The second sentence is represented as
[tex]\neg b[/tex]
The third sentence is represented as
[tex]\neg a[/tex]
So part a can be represented as
[tex]a \to b[/tex]
[tex]\neg b[/tex]
[tex]\neg a[/tex]
Considering part B
Here the objective is to fill in the blank spaces so that the logic of the sentence in part b is as that in part a
Now comparing the second statement a and b
"This program does not contain an error" = "2 is not odd" = [tex]\neg b[/tex]
Hence "this program contains an error." = "2 is odd" = b
Now comparing the third statement a and b
Therefore, it is not the case that all computer programs contain errors.
=
Therefore, it is not the case that all prime numbers are odd
=
[tex]\neg a[/tex]
Hence
If all computer programs contain errors, = if all prime numbers are odd.= a
