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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

Fill in the blank with either ∈ or ∉ to make the statement true.  0 _____ ∅

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.)

Use the Venn diagram to list the elements of the set.  What is the set of students who studied on Saturday and Sunday?

Let  U{“version”:”1.1″,”math”:”U”} = {q, r, s, t, u, v, w, x, y, z}       A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}  List the elements in the set.  A – C

Shade the Venn diagram to represent the set. (A ∪ B ∪ C’ )’

Use a Venn diagram to answer the question. At Nassau Community College there are 551 students taking College Algebra or Calculus. 210 are taking College Algebra, 389 are taking Calculus, and 48 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra?

An example of a genotype is

Let  U{“version”:”1.1″,”math”:”U”} = {q, r, s, t, u, v, w, x, y, z}       A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} List the elements in the set (A ∩ B)’

In the 1980s, what percentage of federal research and development (R&D) funds were going towards military projects?