CSC 133 Test 3 Review

Predicate

A function that returns true or false based on the values of its variables.

Domain

The set of all possible inputs for the variables in a predicate.

Truth Set

The subset of the domain for which the predicate is true.

Universal Quantifier (∀)

Indicates that a predicate is true for all elements within its domain.

Existential Quantifier (∃)

Indicates that there is at least one element in the domain for which the predicate is true.

Rational Number

A number that can be expressed as the quotient of two integers, where the denominator is not zero.

Irrational Number

A number that cannot be represented as a simple fraction, with a non-repeating and non-terminating decimal representation.

Divisibility

An integer a is divisible by another integer b if there exists an integer k such that a = b*k.

Prime Number

A number greater than 1 that has no positive divisors other than 1 and itself.

Quotient-Remainder Theorem

For any integers a and b (b > 0), there exist unique integers q (the quotient) and r (the remainder) such that a = b*q + r, where 0 ≤ r < b.

Absolute Value

The distance of a number from zero on the number line, regardless of direction.

Floor Function

The greatest integer less than or equal to a given number.

Ceiling Function

The smallest integer greater than or equal to a given number.

Tarski’s World

A software program used for modeling and testing theories in first-order logic.

Negating Universal Statements

Converting universal statements into existential statements.

Negating Existential Statements

Converting existential statements into universal statements.

Factoring

The process of breaking down numbers into their prime components.

Unique Factorization Theorem

Every integer greater than 1 can be uniquely factored into prime numbers.

Div and Mod calculations

Operations used to calculate the quotient and remainder when dividing integers.