Question

In each represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a).
a. If all computer programs contain errors, then this program contains an error.
This program does not contain an error.
Therefore, it is not the case that all computer programs contain errors.
b. If _______________, then _____________.
2 is not odd.
Therefore, it is not the case that all prime numbers are odd.

Answer 1

Answer:

a

           $a \to b$

         $\neg b$

         $\neg a$

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   $\neg a$  and $\neg b$ 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 $\to$

Hence the first sentence is denoted as  

         $a \to b$

The  second sentence is represented as

            $\neg b$

The  third sentence is represented as

           $\neg a$

So part a can be represented as

      $a \to b$

         $\neg b$

         $\neg a$

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" = $\neg b$

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  

                                                =

                                                $\neg a$

Hence

If all computer programs contain errors, = if all prime numbers are odd.= a