Discrete Math Exam #2 Review

Predicate

A sentence containing a finite number of variables which becomes a statement when specific values are substituted.

Domain

Set of all values that can be substituted into a predicate.

Truth set

Values in domain that make the statement true.

Universal statement

A statement which is true for every value in the domain.

Existential statement

A statement for which there is at least one value in the domain that makes the statement true.

Negation of a universal statement

Existential statement

Negation of an existential statement

Universal statement

Set

Collection of objects.

Elements of a set

The individual objects in your set.

Subset of a given set

All the objects in the “smaller set” are in the “bigger set.”

Proper subset

All of the elements in one set are in another set, but the bigger set contains at least one element not in A.

Equality of sets

Two sets are equal if A is a subset of B and B is a subset of A. We write A = B.

Disjoint sets

Two sets are said to be disjoint if the intersection is the empty set.

Mutually disjoint sets

A group of sets are mutually disjoint if every possible pairing of sets are disjoint.

Partition of a set

A collection of mutually disjoint sets whose union is the bigger set.

Union of sets

All the elements from multiple sets combined into a larger set.

Intersection of sets

Equal to all the elements included in all the given sets.

Difference of two sets

The relative complement of two sets, written as B-A, is all the elements in B after removing the elements that are also in A.

Complement of a set

The set containing all the elements in the universal set (domain) that are not in the original set.

Natural numbers (N)

The positive integers (whole numbers) 1, 2, 3, etc.

Whole numbers

Any non-negative integer, meaning it's a number without a fractional or decimal part, including zero and all positive integers.

Integers (Z)

Is the number zero, a positive natural number, or the negation of a positive natural number.

Rational numbers (Q)

Any number that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.

Real numbers (R)

Any number that is rational or irrational.