‌Logic – a system of reasoning that Flashcards

1
Q

What is Logic?

A

Logic is a system of reasoning that allows inferences to be drawn from facts.

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2
Q

What is a Proposition?

A

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.

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3
Q

What is a Conjunction?

A

A conjunction is an ‘AND’ statement in mathematics. A conjunction of two statements is true only when both statements are true.

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4
Q

What is a Disjunction?

A

A disjunction is an ‘OR’ statement in mathematics. A disjunction is false if and only if both statements are false; otherwise it is true.

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5
Q

What is Negation?

A

Negation is a ‘NOT’ statement in mathematics. It is a statement with the opposite truth value.

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6
Q

What is a Conditional?

A

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.

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7
Q

What is a Biconditional?

A

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.

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8
Q

What is an Exclusive-or?

A

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.

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9
Q

What are Truth Values of a proposition?

A

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.”

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10
Q

What are Conditional Propositions?

A

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.”

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11
Q

What is the Converse of p-q?

A

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.”

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12
Q

What is the Inverse of p-q?

A

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.”

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13
Q

What is a Contrapositive?

A

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.”

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14
Q

What is a Tautology?

A

A tautology is a proposition that is always true.

Example: “It is either raining or not raining.”

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15
Q

What is a Contradiction?

A

A contradiction is a proposition that is always false.

Example: “It is both raining and not raining.”

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16
Q

What is a Contingency?

A

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.”

17
Q

What is a Proof?

A

A proof is a logical argument that shows a mathematical statement is true.

18
Q

What are Premises?

A

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.”

19
Q

What is a Conclusion?

A

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.”

20
Q

What is Number Theory?

A

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.

21
Q

What is Counting?

A

Counting is a subset of whole numbers that do not include zero.

22
Q

What are Whole Numbers?

A

Whole numbers are a subset of whole numbers that includes the number zero.

23
Q

What are Integers?

A

Integers are whole numbers (not fractional) that can be positive, negative, or zero.

24
Q

What are Rational Numbers?

A

Rational numbers are numbers that can be written as a fraction or a ratio.

25
Q

What are Irrational Numbers?

A

Irrational numbers are numbers that can’t be written as a fraction or ratio.

26
Q

What are Real Numbers?

A

Real numbers are numbers that include both rational and irrational numbers.

27
Q

What are Imaginary Numbers?

A

Imaginary numbers are the product of a real number and the imaginary unit i. When squared, they give a negative result.

28
Q

What are Complex Numbers?

A

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.

29
Q

What are Odd Numbers?

A

Odd numbers are those that cannot be equally divided into pairs and always end with the digits 1, 3, 5, 7, 9.

30
Q

What are Even Numbers?

A

Even numbers are any numbers divisible by 2 and always end with the digits 0, 2, 4, 6, 8.