The Modus Ponens argument

The Modus Ponens argument

 

  1. For the following descriptions, identify the propositions and write the Modus Ponens argument, using propositional variables.

 

  1. If I mow the yard, I won’t wash the car. I’ll mow the yard.  The car won’t get washed.
  2. I’ll order steak and I’ll order potatoes. If I order steak and potatoes instead of salad and diet cola, I’ll be too full for desert.

 

 

  1. Write logical expressions for the following. Be sure to identify the proposition assigned to each propositional variable.

 

  1. Negate the statement, “I will play golf or I will play tennis.”
  2. Find the contrapositive of the statement, “If I study all week, then I will pass my final.”
  3. Find the converse of the statement, “If you don’t buy the DVD, you will have to rent the DVD.”
  4. Write the statement, and the commuted version of, “I can use AutoCAD and Visio.”

 

  1. Is the statement the logical equivalent of   Prove your answer.

 

  1. Evaluate the truth value of the statements. Justify your answer.

 

 

 

  1. Consider the following statements:

 

  1. If I shovel snow, my back aches, and my back aches.
  2. I didn’t shovel snow, or my back doesn’t ache.

 

  1. Translate the sentences into symbols, giving definitions of your propositional variables.
  2. Use a truth table to determine whether the two statements are logically equivalent. State your conclusion.

 

 

 

 

  1. Write the equivalent of  without using the  symbol.

 

  1. Write a truth table to prove the following logical equivalence:

 

  1. Let U = {all people in the United States}. Consider the statement

 

P(x,y) = “x is the mother of y”

 

Evaluate the truth value for these statements (give your rationale).

 

 

 

  1. For the following description, write the logical expression and prove that it is a valid argument. Be sure to identify your propositional variables.

 

I’m not going to buy a Blue-Ray disc of the movie.  I can buy a Blue-Ray disc of the movie or a DVD of the movie.  If I buy a CD, I cannot buy a DVD.  Therefore, I cannot buy a CD.

 

 

  1. Consider the following statements.

 

  1. Consider the following statements. Write a logical argument that shows Steve can barter a pencil and get a car.  Identify your propositional variables.  Order your propositions in your argument in a chronological order, assuming Steve starts out with a pencil.

 

Steve has a pencil.  Steve can fix a car.  Becky will trade her IPod for a DVD.  Bill will trade his pen for a pencil.  Tom will trade a non-running car for a bike.  Myrtle will trade her DVD for a pen.   Mark will trade his bike for an IPod.

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