Test the following argument for validity. If it is invalid,…

Test the following argument for validity. If it is invalid, then create a counterexample chart. If it is valid, then construct a formal proof.  ~p r → p  ~r → (z ∧ s)z    You might want to copy and paste one of these: Statements        Reasons1)                  1) 2)                  2)  (you can continue your own numbers) Or  p r s z

Use the formula for the number of subsets of a set with n el…

Use the formula for the number of subsets of a set with n elements to solve the problem. A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation, no engines, one engine, two engines, three engines, or all four engines can be sent to a fire. How many options does the dispatcher have for sending the fire engines to the scene of the caller? (Hint: Consider every option to be a subset.)