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Translate complex English sentences into propositional and predicate logic
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Translate complex English sentences into symbolic notation
Identify scope and ambiguity in compound statements through linguistic analysis
Represent nested quantifiers and logical structure correctly
Distinguish grammatical form from logical form
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Identify well-formed formulas in propositional and predicate logic
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Recognize well-formed formulas by applying formation rules
Construct well-formed formulas accurately
Explain what makes a formula syntactically correct
Evaluate and correct symbolic strings for well-formedness
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Construct and interpret complete truth tables
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Build complete truth tables for compound formulas
Classify formulas as tautologies, contradictions, or contingencies
Interpret table results to assess consistency
Complete multi-step truth table problems
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Use truth tables to determine validity of propositional arguments
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Apply truth tables to test for argument validity
Identify valid and invalid forms using truth table techniques
Discuss the structure of valid arguments
Determine argument validity from complete truth tables
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Apply inference and replacement rules in propositional logic
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Complete derivations using rules of inference and replacement
Identify correct rule applications
Evaluate derivations for accuracy
Construct formal proofs from given premises
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Use formal rules in predicate logic, including identity and quantifiers
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Construct derivations involving quantifiers and identity
Apply rules for quantifier introduction and elimination
Explain derivation steps involving quantifiers
Solve formal proofs using predicate logic rules
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Construct and analyze truth trees
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Build truth trees to test validity and consistency
Apply decomposition rules accurately
Interpret open and closed branches
Evaluate argument structure using truth trees
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Generate counterexamples to demonstrate invalidity
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Identify invalid argument forms through counterexamples
Construct models that refute argument validity
Justify counterexamples
Analyze arguments and provide counterexamples
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Manipulate quantifiers and distinguish universal and existential claims
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Rewrite statements to clarify quantifier scope
Identify differences between universal and existential claims
Discuss the implications of quantifier order
Apply quantifier manipulation to proofs and translations
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Apply the logic of identity in formal proofs and evaluations
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Use identity introduction and elimination in derivations
Identify errors in identity reasoning
Evaluate the role of identity in logical arguments
Apply identity rules in formal proofs
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Recognize and prove logical equivalence using symbolic techniques
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Derive equivalence through formal rules
Identify equivalent formulas using symbolic criteria
Compare proof strategies for establishing equivalence
Demonstrate logical equivalence through formal proofs
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Distinguish between formal symbolic validity and informal reasoning
Assessment Strategies
Oral or Written product, problem set assignments, quiz, and/or exam
Criteria
Identify formally valid arguments that fail informally
Translate informal arguments and assess symbolic validity
Classify arguments as formally valid or invalid
Evaluate the strengths and limits of symbolic logic