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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 '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?
Which of the following is the correct rule for determining the truth value of a disjunction (or) operation?
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Which of the following is NOT an example of a proposition?
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Which of the following is the correct rule for determining the truth value of a conjunction (and) operation?
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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?
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What kind of proposition is 'The guava is green'?
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Which type of proposition conveys two or more ideas and is formed using logical connectives?
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What does a negation do to a proposition?
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In a compound proposition, what do logical connectives do?
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What does a truth table show for a compound statement?
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What is the truth value of the compound proposition $p \vee \sim q$ when $p$ is true and $q$ is false?
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Which of the following compound propositions is a tautology?
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What is the truth value of the compound proposition $(p \wedge \sim q) \rightarrow q$ when $p$ is false and $q$ is true?
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Which of the following compound propositions is a contradiction?
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What is the truth value of the compound proposition $p \leftrightarrow (p \wedge q)$ when $p$ is true and $q$ is false?
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Which of the following compound propositions is a contingency?
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What type of compound proposition is $p \vee q \wedge \neg p \wedge \neg q$?
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What is the truth value of the compound proposition $p \to q \wedge q \to r \to p \to r$?
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What type of compound proposition is $p \leftrightarrow \neg q \vee \neg r$?
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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?
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Which of the following is a correct statement about the compound proposition $p \to q \wedge q \to r \to p \to r$?
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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?
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What is the truth value of the conditional statement $p \rightarrow q$ when $p$ is true and $q$ is false?
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Which of the following statements is equivalent to the biconditional $p \leftrightarrow q$?
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What is the truth value of the disjunction $p \lor q$ when $p$ is true and $q$ is false?
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Which of the following is the correct order of precedence for logical connectives?
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What is the truth value of the biconditional $p \leftrightarrow q$ when $p$ is true and $q$ is false?
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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
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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.
