Logic chapter 1 basics part 2 Flashcards
(43 cards)
Describe a valid argument using premises and a conclusion.
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.
Define an invalid argument with an example.
Premise 1: Some men are tall. Premise 2: Bob is a man. Conclusion: Bob is tall.
How can you identify a valid argument?
A valid argument is identified by the structure where if the premises are true, the conclusion must also be true.
Do valid arguments guarantee the truth of their premises?
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.
Explain the difference between valid and invalid arguments.
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.
What is the role of premises in an argument?
Premises provide the foundational statements or reasons that support the conclusion in an argument.
How does the conclusion relate to the premises in a valid argument?
In a valid argument, the conclusion logically follows from the premises, meaning that if the premises are true, the conclusion must also be true.
Describe the relationship between the validity of an argument and its premises.
The validity of an argument depends on whether it is possible to make all its premises true and its conclusion false.
Define a sound argument.
A sound argument is one that is valid and has all of its premises true.
How can an argument be valid if all its premises are false?
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.
What is the significance of premises in determining the soundness of an argument?
The premises must be true for an argument to be considered sound, in addition to the argument being valid.
Explain the concept of validity in the context of logical arguments.
Validity refers to the logical structure of an argument, where if the premises are true, the conclusion must also be true.
How does one determine if an argument is invalid?
An argument is invalid if it is possible for all its premises to be true while its conclusion is false.
Define the formal language of TFL.
The formal language of TFL consists of expressions made up of atomic formulas, logical connectives, and brackets.
Describe atomic formulas in TFL.
Atomic formulas in TFL are basic sentences or propositions represented by symbols such as A, B, C, D, etc.
How are logical connectives used in TFL?
Logical connectives in TFL are used to combine atomic formulas to form more complex expressions, including conjunction, disjunction, negation, conditional, and biconditional.
List the logical connectives used in TFL.
The logical connectives used in TFL are conjunction (∧), disjunction (∨), negation (¬), conditional (→), and biconditional (↔).
Explain the meaning of the conjunction operator in TFL.
The conjunction operator (∧) represents the logical operation ‘and’, combining two propositions such that the result is true only if both propositions are true.
What does the disjunction operator signify in TFL?
The disjunction operator (∨) signifies the logical operation ‘or’, which is true if at least one of the propositions is true.
How is negation represented in TFL?
Negation in TFL is represented by the symbol (¬), indicating the opposite truth value of a proposition.
Describe the conditional operator in TFL.
The conditional operator (→) expresses a relationship where if the first proposition is true, then the second proposition must also be true.
What is the biconditional operator in TFL?
The biconditional operator (↔) indicates that two propositions are equivalent, meaning both are true or both are false.
Provide an example of an atomic formula in TFL.
An example of an atomic formula in TFL is A := ‘It is raining in Edmonton’.
Define well-formed formulas in TFL.
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.
