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Questions and Answers
What is the definition of a proposition in logic?
What is the definition of a proposition in logic?
A declarative sentence that is either true or false, but not both.
The sentence 'Is it Tuesday?' is a proposition.
The sentence 'Is it Tuesday?' is a proposition.
False
The sentence 'Go get the car' is a proposition.
The sentence 'Go get the car' is a proposition.
False
The sentence 'This is a nice car.' is a proposition with a definite truth value.
The sentence 'This is a nice car.' is a proposition with a definite truth value.
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Which of the following is NOT a logical connective?
Which of the following is NOT a logical connective?
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What is the symbol for 'not' in logic?
What is the symbol for 'not' in logic?
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What is the symbol for 'if...then' in logic?
What is the symbol for 'if...then' in logic?
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What is the symbol for 'if and only if' in logic?
What is the symbol for 'if and only if' in logic?
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What is the word form for the logical connective symbol 'p A q'?
What is the word form for the logical connective symbol 'p A q'?
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A truth table is a diagram that shows the truth values of propositions and logical connectives.
A truth table is a diagram that shows the truth values of propositions and logical connectives.
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What does the letter 'T' represent in a truth table?
What does the letter 'T' represent in a truth table?
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A tautology is a compound proposition that always results in a TRUE truth value.
A tautology is a compound proposition that always results in a TRUE truth value.
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A contradiction is a compound proposition that always results in a FALSE truth value.
A contradiction is a compound proposition that always results in a FALSE truth value.
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A contingency is a compound proposition that can be either TRUE or FALSE, depending on the truth values of its constituent propositions.
A contingency is a compound proposition that can be either TRUE or FALSE, depending on the truth values of its constituent propositions.
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The negation of a true statement is a false statement.
The negation of a true statement is a false statement.
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The conjunction of two true statements is always a false statement.
The conjunction of two true statements is always a false statement.
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The disjunction of two true statements is always a true statement.
The disjunction of two true statements is always a true statement.
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The implication 'p → q' is false only when p is true and q is false.
The implication 'p → q' is false only when p is true and q is false.
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The biconditional statement 'p ↔ q' is true only when p and q have the same truth value.
The biconditional statement 'p ↔ q' is true only when p and q have the same truth value.
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Study Notes
Learning Objectives
- Students should be able to define logic and its importance in reasoning.
- Students should be able to identify types of statements and their logical properties.
- Students can apply logical connectives to create compound statements.
- Students can analyze arguments for accuracy using truth tables and logical equivalents.
- Students can solve problems that involve logical reasoning.
What is Logic?
- Logic is the study of valid arguments and sound decision-making.
- It is a fundamental tool in mathematics, philosophy, computer science, and daily problem-solving.
Key Concepts: Proposition
- A proposition is a declarative sentence that is either true or false, but not both.
- Propositions are represented by lowercase letters like p, q, r, and s.
Truth Value
- The truth value of a proposition is either True (T) or False (F).
- Examples include:
- p = Manila is the capital of the Philippines. (TRUE)
- q = Dogs are mammals. (TRUE)
- r = It is Tuesday? (Not a proposition; interrogative sentence)
- s = Go get the car. (Not a proposition; imperative sentence)
- t = 8 is a prime number. (FALSE)
Logical Connectives
-
Negation: (~) - "not"
- ~p = "Today is not Sunday"
-
Conjunction: (^) - "and"
- p ^ q = "Today is Sunday and the shop is closed"
-
Disjunction: (v) - "or"
- p v q = "Today is Sunday or the shop is closed"
-
Implication: (→) - "if...then"
- p → q = "If today is Sunday, then the shop is closed"
-
Biconditional: (↔) - "if and only if"
- p ↔ q = "Today is Sunday if and only if the shop is closed"
Types of Propositions
-
Simple: Express a single idea.
- Example: Jonathan likes to play video games.
-
Compound: Express two or more ideas.
- Example: Jonathan likes to play video games and always stays up late.
Summary of Logical Connectives
- A table outlining each connective's word form, statement, and symbolic form.
Truth Tables
- Diagrams showing the relationship between the truth values of propositions in compound propositions(p, q, r).
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Description
This quiz covers the fundamentals of logic, including the definition and importance of logical reasoning. Students will learn about types of statements, truth values, and the application of logical connectives. Engage with various problems that involve logical reasoning to enhance your understanding.
