## APPLICATION OF CRITICAL THINKING & LOGIC

APPLICATION OF CRITICAL THINKING & LOGIC

Paper details:

Create a correct formal proof for the chosen argument from set 3. 1. Provide a line number for each step in your proof. 2. Justify each line in your proof. 3. Use at least one rule of equivalence.

Competency 1007.1.1: Basic Concepts – The graduate applies conceptual foundations of logic and critical thinking to patterns of thinking and reasoning.

Competency 1007.1.2: Logic and Validity – The graduate evaluates arguments, demonstrating validity through application of formal logic and methods.

Competency 1007.1.3: Logic and Critical Thinking – The graduate evaluates sophisticated types of reasoning through the concepts and methods of logic and critical thinking.

Introduction:

For this task you will use tools of natural deduction that you learned from this course. Choose one argument from each of the following three sets. For each argument you chose, provide a proof using the rules of inference you learned in this course. Set 3 will require the use of at least one rule of equivalence in the proof.

Be sure to number and provide a proper justification for each line in your proof.

Set 1

1.P ? Q?RP ? R??Q

2.PQ ? RP ? Q??R

3.Q ? R?RQ ? P??P & ?Q

Set 2

1.P ? QP & R(Q & R) ? S??S

2.(P & Q) ? RQ ? SP & ?S??R

3.P ? (Q ? ?R)P & R??Q

Set 3

1.?P ? QP ? R???R ? Q

2.Q ? PR ? ?P??R ? Q

3.?(?P & ?Q)?Q??P

4.Q ? RP ? (Q & ?R)S ? P??S

Requirements:

A. Create a correct formal proof for the chosen argument from set 1.

1.Provide a line number for each step in your proof.

2.Justify each line in your proof.

B. Create a correct formal proof for the chosen argument from set 2.

1.Provide a line number for each step in your proof.

2.Justify each line in your proof.

C. Create a correct formal proof for the chosen argument from set 3.

1.Provide a line number for each step in your proof.

2.Justify each line in your proof.

3.Use at least one rule of equivalence.

D. When you use sources to support ideas and elements in a paper or project, provide acknowledgement of source information for any content that is quoted, paraphrased or summarized. Acknowledgement of source information includes in-text citation noting specifically where in the submission the source is used and a corresponding reference, which includes:• Author• Date• Title• Location of information (e.g., publisher, journal, or website URL) Note: The use of APA citation style is encouraged but is not required for this task. Evaluators will offer feedback on the acknowledgement of source information but not with regard to conformity with APA or other citation style. For tips on using APA style, please refer to the APA Resources web link found under General Information/APA Guidelines in the left-hand panel in Taskstream. Note: No more than a combined total of 30% of a submission can be directly quoted or closely paraphrased from outside sources, even if cited correctly.

Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link included in the Evaluation Procedures section.