Logic – a system of reasoning that Flashcards
What is Logic?
Logic is a system of reasoning that allows inferences to be drawn from facts.
What is a Proposition?
A proposition is a declarative sentence that is either true or false, but not both.
Example: “Luzon is an island in the Philippines.” This is a TRUE proposition.
What is a Conjunction?
A conjunction is an ‘AND’ statement in mathematics. A conjunction of two statements is true only when both statements are true.
What is a Disjunction?
A disjunction is an ‘OR’ statement in mathematics. A disjunction is false if and only if both statements are false; otherwise it is true.
What is Negation?
Negation is a ‘NOT’ statement in mathematics. It is a statement with the opposite truth value.
What is a Conditional?
A conditional (or implication) is a logical compound statement in which p implies q. The statement is only false when p is true but q is false.
What is a Biconditional?
A biconditional is true when both have the same truth value.
Example: If p and q are both true, then the statement is true. Same goes if p and q are both false.
What is an Exclusive-or?
An exclusive-or statement is true if you are either one but not both. P and q cannot be the same.
Example: I am a dog or I am a cat.
What are Truth Values of a proposition?
The truth value of a proposition is a determination of whether the proposition is true (T) or false (F).
Example: Proposition: “The sun rises in the east.”
What are Conditional Propositions?
Conditional propositions are ‘if-then’ expressions. They are false only when p is true and q is false, and true in all other situations.
Example: “If I study, then I will pass the test.”
What is the Converse of p-q?
The converse of p-q is a conditional proposition in which ‘p implies q’ becomes ‘q implies p’.
Example: Original: “If it rains, the ground is wet.” Converse: “If the ground is wet, it rained.”
What is the Inverse of p-q?
The inverse of p-q is a conditional proposition in which ‘p implies q’ becomes ‘not p implies not q’.
Example: Original: “If it rains, the ground is wet.” Inverse: “If it does not rain, the ground is not wet.”
What is a Contrapositive?
A contrapositive is a conditional proposition in which ‘p implies q’ becomes ‘not p implies not q’.
Example: Original: “If it rains, the ground is wet.” Contrapositive: “If the ground is not wet, it did not rain.”
What is a Tautology?
A tautology is a proposition that is always true.
Example: “It is either raining or not raining.”
What is a Contradiction?
A contradiction is a proposition that is always false.
Example: “It is both raining and not raining.”
What is a Contingency?
A contingency is a proposition that is neither a tautology nor a contradiction; its truth depends on the truth values of its components.
Example: “It is sunny and I will go for a walk.”
What is a Proof?
A proof is a logical argument that shows a mathematical statement is true.
What are Premises?
Premises are statements that are assumed to be true and are used as the basis for an argument.
Example: Premises: “All humans are mortal” and “Socrates is a human.” Conclusion: “Socrates is mortal.”
What is a Conclusion?
A conclusion is a statement that is reached by applying logical rules to a set of premises.
Example: From the premises above, the conclusion is “Socrates is mortal.”
What is Number Theory?
Number theory is a branch of pure mathematics mainly focused on the study of natural numbers and integers.
Example: Proving that there are infinitely many prime numbers.
What is Counting?
Counting is a subset of whole numbers that do not include zero.
What are Whole Numbers?
Whole numbers are a subset of whole numbers that includes the number zero.
What are Integers?
Integers are whole numbers (not fractional) that can be positive, negative, or zero.
What are Rational Numbers?
Rational numbers are numbers that can be written as a fraction or a ratio.
What are Irrational Numbers?
Irrational numbers are numbers that can’t be written as a fraction or ratio.
What are Real Numbers?
Real numbers are numbers that include both rational and irrational numbers.
What are Imaginary Numbers?
Imaginary numbers are the product of a real number and the imaginary unit i. When squared, they give a negative result.
What are Complex Numbers?
Complex numbers are numbers that have two parts: a real part and an imaginary part, denoted by i.
Example: It comes in the form a + ib.
What are Odd Numbers?
Odd numbers are those that cannot be equally divided into pairs and always end with the digits 1, 3, 5, 7, 9.
What are Even Numbers?
Even numbers are any numbers divisible by 2 and always end with the digits 0, 2, 4, 6, 8.
