INSTRUCTIONS: A) Fill out a truth table for the following argument, and then B) state whether the statement is valid or invalid. If the argument is invalid, identify the line(s) that prove that it is invalid. Be sure to identify the main operator of each statement and show all of your work. S  ∨  L   /   L  ⊃  ∼ S   //   S  ∨  ∼ L You may copy the first line of a truth table for this argument from here: S ∨ L / L ⊃ ~ S // S ∨ ~ L

INSTRUCTIONS: A) Fill out a truth table for the following argument, and then B) state whether the statement is valid or invalid. If the argument is invalid, identify the line(s) that prove that it is invalid. Be sure to identify the main operator of each statement and show all of your work. P  ∨  J   /   ∼(J  •  ∼ P)   //   J  ≡  ∼ PYou may copy the first line of a truth table for this argument from here: P ∨ J / ~ (J • ~ P) // J ≡ ~ P

INSTRUCTIONS: The following problems relate to identifying and evaluating inductive and deductive arguments. Select the best answer for each.Pencil lead is composed of pure carbon, and pencil lead is very cheap.  Diamonds, like pencil lead, are composed of pure carbon.  Therefore, probably diamonds are very cheap.

The truth table for the following statement has how many lines? [N  ≡  (S  •  J)]  ⊃  [S  ⊃  (N  ⊃  J)]

INSTRUCTIONS: The following problems relate to identifying and evaluating inductive and deductive arguments. Select the best answer for each.Frank is bringing flowers home to his wife. Apparently Frank is having an affair.

​ INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each.Apple seeds and cherry pits are poisonous because they contain cyanide compounds. Your body can detoxify small quantities of these compounds, but larger doses can lead to difficulty in breathing, increased blood pressure and heart rate, and kidney failure. Reactions can include coma, convulsions, and death from respiratory arrest. Anne Marie Helmstine, “Your Guide to Chemistry”

INSTRUCTIONS: Select the correct translation for each problem.If Disney promotes family cruises, then if either Holland remodels its staterooms or Regent enlarges its casinos, then Windstar diversifies its activities.

INSTRUCTIONS: Compute the truth value of the following proposition, given that A and B are true and X and Y are false (do not complete a truth table for this problem; just use these given values). Be sure to also identify the main operator of the statement and state whether the proposition is true or false. Show all of your work. ∼{[(B  ≡  ∼ X)  ⊃  Y]  ∨  [∼ X  ⊃  (A  ⊃  Y)]}

19) (5 points) Phosphorus-32, used in agriculture, has a half-life of 14 days. 22 milligrams of Phosphorus-32 is present initially in a sample, determine how much Phosophorus-32 is left after 20 days.  How many days will it be till only 5 milligrams of Phosophurus-32 remain in the sample?  

22) (4 points) Solve the system of equations: