determine which of the following arguments are invalid. enter your answer(s) by using the capital letter…

determine which of the following arguments are invalid. enter your answer(s) by using the capital letter that represents each option and separate multiple answers with commas.\na: if you exercise regularly, then you will sleep better. i havent been sleeping better, so i must not be exercising regularly.\nb: if it is raining, then zack is playing video games. zack is playing video games, so it must be raining.\nc: if our team scores a run, then we will play extra innings. we didnt play extra innings, so our team must not have scored a run.\nd: if mike does his chores, then his mom will give him fifty dollars. mikes mom gave him fifty dollars, so he must have done his chores.

determine which of the following arguments are invalid. enter your answer(s) by using the capital letter that represents each option and separate multiple answers with commas.\na: if you exercise regularly, then you will sleep better. i havent been sleeping better, so i must not be exercising regularly.\nb: if it is raining, then zack is playing video games. zack is playing video games, so it must be raining.\nc: if our team scores a run, then we will play extra innings. we didnt play extra innings, so our team must not have scored a run.\nd: if mike does his chores, then his mom will give him fifty dollars. mikes mom gave him fifty dollars, so he must have done his chores.

Answer

Brief Explanations:

  • For argument A:
    • Let (p) be "you exercise regularly" and (q) be "you will sleep better". The form is (p\rightarrow q), (\neg q), so (\neg p). This is Modus Tollens (a valid form).
  • For argument B:
    • Let (p) be "it is raining" and (q) be "Zack is playing video games". The form is (p\rightarrow q), (q), so (p). This is Affirming the Consequent (an invalid form).
  • For argument C:
    • Let (p) be "our team scores a run" and (q) be "we will play extra innings". The form is (p\rightarrow q), (\neg q), so (\neg p). This is Modus Tollens (a valid form).
  • For argument D:
    • Let (p) be "Mike does his chores" and (q) be "his mom will give him fifty dollars". The form is (p\rightarrow q), (q), so (p). This is Affirming the Consequent (an invalid form).

Answer:

B, D