Symbolic Logic

Learning Topics: 

Negation, conjunction, disjunction, conditional, compound statements, biconditionals, tautologies and equivalence.

This page lists the Learning Objectives for all 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.