Propositional Logic
1 hr 33 min 25 Examples
- What is a proposition? paradox? open sentence? with Examples #1-9
- What is Symbolic Logic? What are common connectives?
- Negate each statement (Examples #10-13)
- Determine if “inclusive or” or “exclusive or” is intended (Example #14)
- Translate the symbolic logic into English (Example #15)
- Convert the English sentence into symbolic logic (Example #16)
- Determine the truth value of each proposition (Example #17)
- How do we create a truth table? (Example #18)
- Construct a truth table for each statement (Examples #19-20)
- Create a truth table for each proposition (Examples #21-24)
- Form a truth table for the following statement (Example #25)
Logical Implication
1 hr 16 min 15 Examples
- What are conditional statements? Properties? and How do we write them? (Examples #1-2)
- Express each statement using logical connectives and determine the truth of each implication (Examples #3-4)
- Finding the converse, inverse, and contrapositive (Example #5)
- Write the implication, converse, inverse and contrapositive (Example #6)
- What are the properties of biconditional statements and the six propositional logic sentences?
- Write a biconditional statement and determine the truth value (Example #7-8)
- Construct a truth table for each compound, conditional statement (Examples #9-12)
- Create a truth table for each (Examples #13-15)
Logical Equivalence
1 hr 4 min 14 Examples
- What is a Tautology? Contradiction? Contingency?
- How do we show propositional Equivalence? (Examples #1-3)
- Equivalence Laws
- Equivalence Laws for Conditional and Biconditional Statements
- Use De Morgan’s Laws to find the negation (Example #4)
- Provide the logical equivalence for the statement (Examples #5-8)
- Show that each conditional statement is a tautology (Examples #9-11)
- Use a truth table to show logical equivalence (Examples #12-14)
Predicate Logic
1 hr 20 min 23 Examples
- What is predicate logic? What is Quantification? (Examples #1-2)
- Understanding Universal and Existential Quantifiers
- Transform each sentence using predicates, quantifiers and symbolic logic (Example #3)
- Determine the truth value for each quantified statement (Examples #4-12)
- How to Negate Quantified Statements? (Examples #13-14)
- Find the negation of each quantified statement (Examples #15-18)
- Translate from predicates and quantifiers into English (#19-20)
- Convert predicates, quantifiers and negations into symbols (Example #21)
- Determine the truth value for the quantified statement (Example #22)
- Express into words and determine the truth value (Example #23)
Rules of Inference
1 hr 33 min 7 Examples
- Understanding logical arguments
- Inference Rules with tautologies and examples
- What rule of inference is used in each argument? (Example #1a-e)
- Determine the logical conclusion to make the argument valid (Example #2a-e)
- Write the argument form and determine its validity (Example #3a-f)
- Rules of Inference for Quantified Statement
- Determine if the quantified argument is valid (Example #4a-d)
- Given the predicates and domain, choose all valid arguments (Examples #5-6)
- Construct a valid argument using the inference rules (Example #7)
Categorical Syllogism
58 min 12 Examples
- What are the types of propositions, mood, and steps for diagraming categorical syllogism?
- Use Venn diagrams to determine if the categorical syllogism is valid or invalid (Examples #1-4)
- Determine if the categorical syllogism is valid or invalid and diagram the argument (Examples #5-8)
- Identify if the proposition is valid (Examples #9-12)
Chapter Test
1 hr 8 min 9 Practice Problems
- Which of the following is a proposition? (Problem #1)
- Determine the truth value of the given statements (Problem #2)
- Convert each statement into symbols (Problem #3)
- Express the following in words (Problem #4)
- Write the converse and contrapositive of each of the following (Problem #5)
- Decide whether each of following arguments are valid (Problem #6
- Negate the following statements (Problem #7)
- Create a truth table for each (Problem #8)
- Use a truth table to show equivalence (Problem #9)