This page lists the Learning Objectives for each core lesson in Unit 9
of 13.
Negation
The student will be able to:
- Define closed sentences, open sentences, statements, negation, truth value, and truth tables.
- List a simple sentence in symbolic form.
- Identify a sentence as true, false or open.
- List the negation of a statement in symbolic form and in sentence form.
- Recognize that a statement and its negation have opposite truth values.
- List the truth values for a given statement and its negation.
- Apply negation concepts to solve logic problems.
Conjunction
The student will be able to:
- Define logical connectors, compound statements, and conjunctions.
- List 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.
- List 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.
- Apply conjunction concepts to solve logic problems.
Disjunction
The student will be able to:
- Define disjunctions.
- List 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.
- List the truth values for a conjunction, given the truth values of each part.
- Construct a truth table for a disjunction to determine its truth values.
- Given two statements, construct a truth table for their conjunction and disjunction.
- Apply disjunction concepts to solve logic problems.
Conditional
The student will be able to:
- Define conditional statements, an hypothesis, and conclusions.
- Identify the hypothesis and conclusion of a conditional statement.
- List a conditional statement in symbolic form and in sentence form.
- List the truth value of a conditional statement, given the truth value of each part.
- Apply conditional logic concepts to solve problems.
Compound Statements
The student will be able to:
- Define symbolic form.
- Evaluate sentences represented by compound statements with the connectors
~,
,
,and
.
- List a compound statement in symbolic form with the connectors ~, ,,and
.
- List the truth value of a compound statement, given the truth values of each part.
- Construct a truth table for a compound statement to determine its truth values.
- Apply compound statement concepts to solve logic problems.
Biconditional
The student will be able to:
- Define biconditional statements.
- List a biconditional in symbolic form, and in sentence form using "if and only if" or "iff".
- Identify the hypothesis and the conclusion of a biconditional.
- Evaluate a sentence to determine whether or not it is biconditional.
- Recognize the difference between a conditional and a biconditional statement.
- Apply biconditional concepts to solve logic problems.
Tautologies
The student will be able to:
- Define tautologies.
- Identify the individual parts of a compound statement.
- Construct a truth table for a compound statement to determine whether or not it is a tautology.
- Apply tautology concepts to solve logic problems.
Equivalent Statements
The student will be able to:
- Define logical equivalence.
- Construct a truth table for several compound statements to determine which two are logically equivalent.
- Recognize that the biconditional of two equivalent statements is a tautology.
- Apply equivalence concepts to solve logic problems.
Practice Exercises
The student will be able to:
- Identify the concepts and procedures needed to solve each problem.
- Apply logic concepts and construct truth tables to solve simple problems.
Challenge Exercises
The student will be able to:
- Analyze each problem to identify the given information.
- Identify the concepts and procedures needed to solve each problem.
- Apply logic concepts to solve complex problems.
- Develop strong problem-solving skills.
Solutions
The student will be able to:
- Analyze the solution for each exercise presented in this unit.
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