# Critical Thinking Assignment

**Paper, Order, or Assignment Requirements**

Complete the following exercises from the text:

**5.1 #3 For each of the following propositions, determine each of the propositional forms for which it is a uniform substitution instance.**

**f)**~A É (~B É ~A)**g)**(A Ú B) É (C Ú D)**i)**(~A Ú B) É (~A Ú D)

**6.1: #2 (d)** [4 points]

**Using truth tables, prove that the argument form corresponding to each of the following conditional transformation rules is valid: Hypothetical Syllogism.**

** **

**6.2: #1 Using the transformation rules of System P, prove each of the following arguments to be valid:**

**(g)** [4 points]

**A ****É**** (B ****Ù**** C)**

**D**

__~C__________

**D ****Ù**** ~A**

** **

**(h)** [6 points]

**A ****É**** (B ****Ù**** C)**

**A ****É**** (D ****Ù**** E)**

**E ****É**** ~C**

**________**

**~A**

** **

**#3 Formalize the following natural language arguments, then prove them to be valid using the transformation rules of System P. **

**(d)** [6 points]

Bill parked his car in either the blue lot or the red lot. If he parked it in the blue lot then it would still be there. But it’s not. So, he must have parked it in the red lot.

**6.3: #1**

**Using the rules of inference for System P, prove the following arguments to be truth-functionally valid. **

**(d)** [8]

**A ****Ù**** B**

**~D**

**_________**

**C ****É**** [~(A ****Ù**** D) ****Ù**** B]**

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