Purpose of Assignment:

To help you…

1. learn the syntax of propositional logic formulas
2. determine the meaning (determine the truth value) of a propositional logic formula using truth tables
3. understand the correspondence between
   • proposition logic formulas and circuits, and
   • tracing the execution of a circuit and building a truth table
4. become acquainted with the Logika tool

We have created some automated grading tools to speed the grading of homeworks. To apply those tools, we need to make sure that each student uses a consistent naming for all their solutions file. Therefore, we have created an IntelliJ project with template files for your solution. DON’T CHANGE THE NAME OF ANY OF THE FILES that we give you.

Getting started

You can find examples of completed Logika truth tables in the Logika example repository (included in the class examples that you downloaded (as illustrated in the “Step #2” videos). Here is a direct link to the truth table portion of those examples:https://github.com/sireum/v3-logika-examples/tree/release/src/truthtable

Considerations

1. All files must run in the Sireum IVE
2. To receive any points a problem must:

• be a Logika Truth Table (see examples and class slides)
• contain the proper logic proposition
• identify the correct logical connective with an *
• i.e. you must answer the correct question

1. Partial credit may be received if

• Some truth assignments are incorrect
• There are errors in the Tautology/Contradictory/Contingent section

1. Do not change the variable name
2. List all variables alphabetically ( “p q r” not “r p q” )

Problems

1. (4 points) Write the truth table for the proposition below:¬p → q V r
2. (3 points) To see the impact of precedence, write the truth table for:¬(p → q) V r
3. (4 points) Write the truth table for:(p → q) ∧ (q → r)
4. (5 points) Write a truth table for the following circuit:
5. (11 points) Consider the two propositions below. Are they equivalent?Justify your answer with appropriate truth tables and a short supportingcomment. Comments in Logika, like C, begin with //.(p → q)→ rp → (q → r)
6. (3 points) Using two variables p and q, write a logical proposition andtruth table for a Tuatology.