Podcast
Questions and Answers
What is the truth value of the compound proposition 'Bacolod City is the capital city of the Philippines or Tokyo is the capital city of Japan' given that 'Bacolod City is the capital city of the Philippines' is false and 'Tokyo is the capital city of Japan' is true?
What is the truth value of the compound proposition 'Bacolod City is the capital city of the Philippines or Tokyo is the capital city of Japan' given that 'Bacolod City is the capital city of the Philippines' is false and 'Tokyo is the capital city of Japan' is true?
What is the truth value of the compound proposition '7 > 0 and 0 < -1' given that '7 > 0' is true and '0 < -1' is false?
What is the truth value of the compound proposition '7 > 0 and 0 < -1' given that '7 > 0' is true and '0 < -1' is false?
What is the truth value of the compound proposition 'If 0.2 is not an integer, then it is a natural number' given that '0.2 is not an integer' is false and '0.2 is a natural number' is false?
What is the truth value of the compound proposition 'If 0.2 is not an integer, then it is a natural number' given that '0.2 is not an integer' is false and '0.2 is a natural number' is false?
Which of the following is the correct rule for determining the truth value of a disjunction (or) operation?
Which of the following is the correct rule for determining the truth value of a disjunction (or) operation?
Signup and view all the answers
Which of the following is NOT an example of a proposition?
Which of the following is NOT an example of a proposition?
Signup and view all the answers
Which of the following is the correct rule for determining the truth value of a conjunction (and) operation?
Which of the following is the correct rule for determining the truth value of a conjunction (and) operation?
Signup and view all the answers
What is the correct rule for determining the truth value of an implication (if-then) operation when the antecedent is false and the consequent is false?
What is the correct rule for determining the truth value of an implication (if-then) operation when the antecedent is false and the consequent is false?
Signup and view all the answers
What kind of proposition is 'The guava is green'?
What kind of proposition is 'The guava is green'?
Signup and view all the answers
Which type of proposition conveys two or more ideas and is formed using logical connectives?
Which type of proposition conveys two or more ideas and is formed using logical connectives?
Signup and view all the answers
What does a negation do to a proposition?
What does a negation do to a proposition?
Signup and view all the answers
In a compound proposition, what do logical connectives do?
In a compound proposition, what do logical connectives do?
Signup and view all the answers
What does a truth table show for a compound statement?
What does a truth table show for a compound statement?
Signup and view all the answers
What is the truth value of the compound proposition $p \vee \sim q$ when $p$ is true and $q$ is false?
What is the truth value of the compound proposition $p \vee \sim q$ when $p$ is true and $q$ is false?
Signup and view all the answers
Which of the following compound propositions is a tautology?
Which of the following compound propositions is a tautology?
Signup and view all the answers
What is the truth value of the compound proposition $(p \wedge \sim q) \rightarrow q$ when $p$ is false and $q$ is true?
What is the truth value of the compound proposition $(p \wedge \sim q) \rightarrow q$ when $p$ is false and $q$ is true?
Signup and view all the answers
Which of the following compound propositions is a contradiction?
Which of the following compound propositions is a contradiction?
Signup and view all the answers
What is the truth value of the compound proposition $p \leftrightarrow (p \wedge q)$ when $p$ is true and $q$ is false?
What is the truth value of the compound proposition $p \leftrightarrow (p \wedge q)$ when $p$ is true and $q$ is false?
Signup and view all the answers
Which of the following compound propositions is a contingency?
Which of the following compound propositions is a contingency?
Signup and view all the answers
What type of compound proposition is $p \vee q \wedge \neg p \wedge \neg q$?
What type of compound proposition is $p \vee q \wedge \neg p \wedge \neg q$?
Signup and view all the answers
What is the truth value of the compound proposition $p \to q \wedge q \to r \to p \to r$?
What is the truth value of the compound proposition $p \to q \wedge q \to r \to p \to r$?
Signup and view all the answers
What type of compound proposition is $p \leftrightarrow \neg q \vee \neg r$?
What type of compound proposition is $p \leftrightarrow \neg q \vee \neg r$?
Signup and view all the answers
In the truth table for $p \vee q \wedge \neg p \wedge \neg q$, what is the truth value of the expression when $p$ is true and $q$ is true?
In the truth table for $p \vee q \wedge \neg p \wedge \neg q$, what is the truth value of the expression when $p$ is true and $q$ is true?
Signup and view all the answers
Which of the following is a correct statement about the compound proposition $p \to q \wedge q \to r \to p \to r$?
Which of the following is a correct statement about the compound proposition $p \to q \wedge q \to r \to p \to r$?
Signup and view all the answers
In the truth table for $p \leftrightarrow \neg q \vee \neg r$, what is the truth value of the expression when $p$ is false, $q$ is true, and $r$ is false?
In the truth table for $p \leftrightarrow \neg q \vee \neg r$, what is the truth value of the expression when $p$ is false, $q$ is true, and $r$ is false?
Signup and view all the answers
What is the truth value of the conditional statement $p \rightarrow q$ when $p$ is true and $q$ is false?
What is the truth value of the conditional statement $p \rightarrow q$ when $p$ is true and $q$ is false?
Signup and view all the answers
Which of the following statements is equivalent to the biconditional $p \leftrightarrow q$?
Which of the following statements is equivalent to the biconditional $p \leftrightarrow q$?
Signup and view all the answers
What is the truth value of the disjunction $p \lor q$ when $p$ is true and $q$ is false?
What is the truth value of the disjunction $p \lor q$ when $p$ is true and $q$ is false?
Signup and view all the answers
Which of the following is the correct order of precedence for logical connectives?
Which of the following is the correct order of precedence for logical connectives?
Signup and view all the answers
What is the truth value of the biconditional $p \leftrightarrow q$ when $p$ is true and $q$ is false?
What is the truth value of the biconditional $p \leftrightarrow q$ when $p$ is true and $q$ is false?
Signup and view all the answers
Study Notes
Fundamentals of Logic
- A proposition is a declarative statement that is either true or false, but cannot be both.
- A proposition has a truth value.
- Examples of propositions:
- Washington D.C. is the capital city of the United States of America. (TRUE)
- Toronto City is the capital city of Canada. (FALSE)
- 1 + 1 = 2 (TRUE)
- 2 + 5 = 6 (FALSE)
Types of Propositions
- Simple Proposition: Conveys a single idea.
- Examples: The guava is green. x - 10 = 5
- Compound Proposition: Conveys two or more ideas and is formed using logical connectives.
- Examples: I will eat or I will sleep. 10 is even and greater than 5. If 2x + 3 = 1, then x = -1
Truth Tables
- A truth table is a table that shows the truth values of a compound statement for all possible truth values of its simple statements.
- Truth Table of a Negation: Negation introduces the word "not" to the proposition, thus reversing its meaning, thus the term "negate".
- Example: Find the truth values of p ∨ ~q using a truth table.
Sequence of Logical Connectives
- Example: Find the truth values of p ∨ ~q using a truth table.
- Example: Find the truth values of p ↔ p ∧ q using a truth table.
- Example: Find the truth values of p ∧ ~q → q using a truth table.
- Example: Find the truth values of p ∧ q → ~r using a truth table.
Types of Compound Propositions
- Tautology: A compound proposition that is true in all cases.
- Contradiction: A compound proposition that is false in all cases.
- Contingency: A compound proposition that is a combination of true and false.
- Example: Find the truth values of p ∨ q ∧ ~p ∧ ~q proposition using a truth table. Determine the type of compound proposition.
Truth Table of an Implication or Conditional
- "p → q" is read as "if p, then q".
- The conditional p → q is false if p is true and q is false.
- It is true in all other cases.
Truth Table of a Bi-implication or Biconditional
- "p ↔ q" is read as "p if and only if q".
- The biconditional p ↔ q is true if both p and q are true or both p and q are false.
- It is false in all other cases.
Summary of Logical Connectives
- Logical Connective: Read as Symbol: Truth Value
- Conjunction: and ∧: True if both propositions are true
- Disjunction: or ∨: False if both propositions are false
- Conditional: if … then … →: False if first proposition is true and second proposition is false
- Biconditional: if and only if ↔: True if both propositions are true or both propositions are false
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on propositions, which are declarative statements that can either be true or false. Learn about truth values and examples of propositions in this quiz.
