# Symbolic Logic

## Learning Objectives for all Symbolic Logic Lessons in Unit 9.

**Negation**

The student will be able to:

- Define closed sentence, open sentence, statement, negation, truth value and truth tables.
- Example examples in which a simple sentence is written in symbolic form.
- Determine if a sentence is true, false or open.
- Express the negation of a statement in symbolic form and in sentence form.
- Recognize that a statement and its negation have opposite truth values.
- Determine the truth values for a given statement and its negation.
- Construct a truth table to summarize truth values.
- Connect negation with written English.
- Apply negation concepts to complete five interactive exercises.

**Conjunction**

The student will be able to:

- Define logical connector, compound statement and conjunction.
- Express a conjunction in symbolic form and in sentence form.
- Recognize that the conjunction of two open sentences depends on the replacement value of the variable in each.
- Determine the truth values of a conjunction, given the truth values of each part.
- Construct a truth table for a conjunction to determine its truth values.
- Recognize that a truth table is an excellent tool for summarizing the truth values of statements.
- Integrate conjunction with other topics in mathematics.
- Apply conjunction concepts to complete five interactive exercises.

**Disjunction**

The student will be able to:

- Define disjunction.
- Express a disjunction in symbolic form and in sentence form.
- Recognize that the disjunction of two open sentences depends on the replacement value of the variable in each.
- Determine the truth values for a disjunction, given the truth values of each part.
- Construct a truth table for a disjunction to determine its truth values.
- Construct a truth table for the conjunction and disjunction of two statements.
- Distinguish between a disjunction and a conjunction.
- Integrate disjunction with other topics in mathematics.
- Apply disjunction concepts to complete five interactive exercises.

**Conditional**

The student will be able to:

- Define conditional statement, hypothesis and conclusion.
- Identify the hypothesis and conclusion of a conditional statement.
- Express a conditional statement in symbolic form and in sentence form.
- Construct a truth table for a conditional statement.
- Determine the truth value of the conditional, given the truth values of its hypothesis and conclusion.
- Integrate conditional statements with other topics in mathematics.
- Apply conditional concepts to complete five interactive exercises.

**Compound Statements**

The student will be able to:

- Define symbolic form.
- Examine sentences represented by compound statements with the connectors ~, ,,and .
- Express compound statements in symbolic form with the connectors ~, ,,and .
- Determine the truth value of a compound statement, given the truth values of each part.
- Construct a truth table for a compound statement, given in symbolic form, to determine its truth values.
- Integrate compound statements with other topics in mathematics.
- Apply compound statement concepts to complete five interactive exercises.

**Biconditional**

The student will be able to:

- Define biconditional statement.
- Given a hypothesis and a conclusion, construct a biconditional statement in sentence form
- Given a hypothesis and a conclusion, construct a biconditional statement in sentence in symbolic form.
- Given a hypothesis and a conclusion, construct a truth table for the biconditional statement.
- Express biconditional statements using “if and only if” or “iff”.
- Explain the relationship between a conditional and a biconditional statement.
- Integrate biconditional statements with other topics in mathematics.
- Apply biconditional concepts to complete five interactive exercises.

**Tautologies**

The student will be able to:

- Review disjunction, negation and compound statements.
- Define tautology.
- Decipher the individual parts of a compound statement.
- Determine if a compound statement is a tautology by constructing a truth table for its individual parts.
- Apply tautology concepts to complete five interactive exercises.

**Equivalent Statements**

The student will be able to:

- Define logical equivalence.
- Construct a truth table for three compound statements to determine which two are logically equivalent.
- Recognize that the biconditional of two equivalent statements is a tautology.
- Apply equivalence concepts to complete five interactive exercises.

**Practice Exercises**

The student will be able to:

- Examine ten interactive exercises for all topics in this unit.
- Determine which concepts and procedures are needed to complete each practice exercise.
- Complete interactive truth tables by applying concepts and procedures from symbolic logic.
- Compute answers by applying concepts and procedures from symbolic logic.
- Self-assess knowledge and skills acquired from this unit.

**Challenge Exercises**

The student will be able to:

- Evaluate ten interactive exercises for all topics in this unit.
- Analyze each problem to identify the given information.
- Determine the truth values of compound statements.
- Apply logic concepts to solve complex problems.

**Solutions**

The student will be able to:

- Examine the solution for each exercise presented in this unit.
- Identify which solutions need to be reviewed.
- Compare solutions to completed exercises.
- Identify and evaluate incorrect answers.
- Repeat exercises that were incorrectly answered.
- Identify areas of strength and weakness.
- Decide which concepts and procedures need to be reviewed from this unit.