Lecture 3 Flashcards
(18 cards)
What is formal logic?
A system of reasoning that uses formal principles to evaluate arguments and statements
Formal logic distinguishes between valid and invalid arguments through structured propositions and connectives.
What does ‘AND’ (Conjunction) signify in formal logic?
It connects two ideas or statements where both must be true
Example: ‘The essay is well-organized, and the author has used strong arguments.’
What does ‘OR’ (Disjunction) signify in formal logic?
At least one of the connected statements must be true
Example: ‘Either I will study today, or I will study tomorrow.’
What does ‘NOT’ (Negation) signify in formal logic?
It indicates that a statement is false
Example: ‘It is not raining.’
What does ‘IF…THEN’ (Conditional) signify in formal logic?
It expresses a cause-and-effect relationship between two statements
Example: ‘If I study hard, then I will pass the test.’
What does ‘IF AND ONLY IF’ (Biconditional) signify in formal logic?
Both statements are true in a specific way; if one is true, the other must be true, and vice versa
Example: ‘I will go to the party if and only if my friend goes too.’
What is Modus Ponens?
A rule of inference stating if the first statement is true, then the second must also be true
Structure: If p, then q; p is true; therefore, q is true.
Provide the structure of Modus Ponens.
Premise 1: If p, then q; Premise 2: p is true; Conclusion: therefore, q is true
What is Modus Tollens?
A rule of inference stating if the first statement implies the second, and the second is false, then the first must also be false
Structure: If p, then q; q is false; therefore, p is false.
Provide the structure of Modus Tollens.
Premise 1: If p, then q; Premise 2: q is false; Conclusion: therefore, p is false
What is Disjunctive Syllogism?
A rule of inference stating if at least one of two statements is true and one is false, then the other must be true
Structure: p or q; not p; therefore, q must be true.
Provide the structure of Disjunctive Syllogism.
Premise 1: p or q; Premise 2: Not p; Conclusion: therefore, q must be true
What is the conclusion of Modus Ponens?
If p is true, then q is true
Example: If I study, then I will pass. I studied. Therefore, I will pass.
What is the conclusion of Modus Tollens?
If q is false, then p is false
Example: If I study, then I will pass. I did not pass. Therefore, I did not study.
What is the conclusion of Disjunctive Syllogism?
If not p, then q must be true
Example: I will either go to the gym or the library. I did not go to the gym. Therefore, I went to the library.
Fill in the blank: Modus Ponens states that if p → q, and p is true, then _______ is true.
q
Fill in the blank: Modus Tollens states that if p → q, and q is false, then _______ is false.
p
Fill in the blank: Disjunctive Syllogism states that if p ∨ q, and not p, then _______ must be true.
q
