## The Modus Ponens argument

## The Modus Ponens argument

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

- If I mow the yard, I won’t wash the car. I’ll mow the yard. The car won’t get washed.
- 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.

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

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

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

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

- Consider the following statements:

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

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

- Write the equivalent of without using the symbol.

- Write a truth table to prove the following logical equivalence:

- 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).

- 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.

- Consider the following statements.

- 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.