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LOGIC 125 > Logic chapter 1 basics part 2 > Flashcards

Logic chapter 1 basics part 2 Flashcards

1
Q

Describe a valid argument using premises and a conclusion.

A

Premise 1: Either the Butler or the housemaid stole the vase. Premise 2: The housemaid did not steal the vase. Conclusion: The butler stole the vase.

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2
Q

Define an invalid argument with an example.

A

Premise 1: Some men are tall. Premise 2: Bob is a man. Conclusion: Bob is tall.

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3
Q

How can you identify a valid argument?

A

A valid argument is identified by the structure where if the premises are true, the conclusion must also be true.

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4
Q

Do valid arguments guarantee the truth of their premises?

A

No, valid arguments do not guarantee the truth of their premises; they only ensure that if the premises are true, the conclusion must be true.

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5
Q

Explain the difference between valid and invalid arguments.

A

Valid arguments have a logical structure that ensures the conclusion follows from the premises, while invalid arguments do not guarantee that the conclusion is true even if the premises are true.

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6
Q

What is the role of premises in an argument?

A

Premises provide the foundational statements or reasons that support the conclusion in an argument.

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7
Q

How does the conclusion relate to the premises in a valid argument?

A

In a valid argument, the conclusion logically follows from the premises, meaning that if the premises are true, the conclusion must also be true.

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8
Q

Describe the relationship between the validity of an argument and its premises.

A

The validity of an argument depends on whether it is possible to make all its premises true and its conclusion false.

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9
Q

Define a sound argument.

A

A sound argument is one that is valid and has all of its premises true.

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10
Q

How can an argument be valid if all its premises are false?

A

An argument can be valid if it is structured in such a way that it is logically consistent, regardless of the truth value of its premises.

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11
Q

What is the significance of premises in determining the soundness of an argument?

A

The premises must be true for an argument to be considered sound, in addition to the argument being valid.

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12
Q

Explain the concept of validity in the context of logical arguments.

A

Validity refers to the logical structure of an argument, where if the premises are true, the conclusion must also be true.

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13
Q

How does one determine if an argument is invalid?

A

An argument is invalid if it is possible for all its premises to be true while its conclusion is false.

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14
Q

Define the formal language of TFL.

A

The formal language of TFL consists of expressions made up of atomic formulas, logical connectives, and brackets.

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15
Q

Describe atomic formulas in TFL.

A

Atomic formulas in TFL are basic sentences or propositions represented by symbols such as A, B, C, D, etc.

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16
Q

How are logical connectives used in TFL?

A

Logical connectives in TFL are used to combine atomic formulas to form more complex expressions, including conjunction, disjunction, negation, conditional, and biconditional.

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17
Q

List the logical connectives used in TFL.

A

The logical connectives used in TFL are conjunction (∧), disjunction (∨), negation (¬), conditional (→), and biconditional (↔).

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18
Q

Explain the meaning of the conjunction operator in TFL.

A

The conjunction operator (∧) represents the logical operation ‘and’, combining two propositions such that the result is true only if both propositions are true.

19
Q

What does the disjunction operator signify in TFL?

A

The disjunction operator (∨) signifies the logical operation ‘or’, which is true if at least one of the propositions is true.

20
Q

How is negation represented in TFL?

A

Negation in TFL is represented by the symbol (¬), indicating the opposite truth value of a proposition.

21
Q

Describe the conditional operator in TFL.

A

The conditional operator (→) expresses a relationship where if the first proposition is true, then the second proposition must also be true.

22
Q

What is the biconditional operator in TFL?

A

The biconditional operator (↔) indicates that two propositions are equivalent, meaning both are true or both are false.

23
Q

Provide an example of an atomic formula in TFL.

A

An example of an atomic formula in TFL is A := ‘It is raining in Edmonton’.

24
Q

Define well-formed formulas in TFL.

A

Well-formed formulas in TFL are defined inductively, including any atomic formula as a formula, negation of a formula, and combinations of formulas using conjunction, disjunction, implication, and biconditional.

25
Q

Describe the process of constructing complex formulas in TFL.

A

Complex formulas in TFL can be constructed from basic ones through operations such as negation, conjunction, disjunction, implication, and biconditional.

26
Q

How is negation represented in TFL formulas?

A

Negation in TFL formulas is represented by the symbol ¬, indicating the negation of a formula A as ¬A.

27
Q

What are the symbols used for conjunction and disjunction in TFL?

A

In TFL, conjunction is represented by the symbol ∧ and disjunction by the symbol ∨.

28
Q

Explain the significance of atomic formulas in TFL.

A

Atomic formulas serve as the basic building blocks for constructing more complex well-formed formulas in TFL.

29
Q

List the operations that can be applied to formulas in TFL.

A

The operations that can be applied to formulas in TFL include negation (¬), conjunction (∧), disjunction (∨), implication (→), and biconditional (↔).

30
Q

Provide an example of a well-formed formula in TFL.

A

An example of a well-formed formula in TFL is A → (B ∨ C).

31
Q

Identify an expression that is not a well-formed formula in TFL.

A

An example of an expression that is not a well-formed formula in TFL is ¬ ∨ A.

32
Q

How can you determine if a formula is well-formed in TFL?

A

A formula is well-formed in TFL if it can be constructed using the defined operations on atomic formulas according to the inductive rules.

33
Q

Describe the role of the biconditional operator in TFL formulas.

A

The biconditional operator (↔) in TFL formulas indicates that two formulas are equivalent, meaning both are true or both are false.

34
Q

Describe the order of precedence for logical connectives in TFL.

A

The order of precedence for logical connectives in TFL is as follows: 1. Parentheses (highest precedence), 2. Negation (¬), 3. Conjunction (∧), 4. Disjunction (∨), 5. Implication (→), 6. Biconditional (↔) (lowest precedence).

35
Q

How does the order of precedence affect the evaluation of logical expressions?

A

The order of precedence determines the sequence in which logical operations are performed in an expression, ensuring that certain operations are evaluated before others to avoid ambiguity.

36
Q

Define the highest precedence logical connective in TFL.

A

The highest precedence logical connective in TFL is the parentheses, which dictate the grouping of expressions.

37
Q

Explain the significance of using parentheses in logical expressions.

A

Using parentheses in logical expressions clarifies the intended order of operations, ensuring that the expression is evaluated correctly according to the established precedence.

38
Q

What is the lowest precedence logical connective in TFL?

A

The lowest precedence logical connective in TFL is the biconditional (↔).

39
Q

How would you write the expression A ∧ B → C with proper precedence?

A

The expression should be written as (A ∧ B) → C to indicate the correct order of operations.

40
Q

Describe the role of negation in the order of precedence.

A

Negation (¬) has the second highest precedence in TFL, meaning it is evaluated before conjunction (∧) and disjunction (∨) but after parentheses.

41
Q

What is the relationship between conjunction and disjunction in terms of precedence?

A

In terms of precedence, conjunction (∧) is evaluated before disjunction (∨) in logical expressions.

42
Q

How would you express the logical statement involving multiple connectives correctly?

A

To express a logical statement involving multiple connectives correctly, use parentheses to group operations according to their precedence, such as ((A ∧ B) → (C ∨ D)) ↔ E.

43
Q

Define implication in the context of logical connectives.

A

Implication (→) is a logical connective that indicates a conditional relationship between two statements, where the truth of one statement implies the truth of another.

LOGIC 125 (7 decks)

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