Math Test 1

disjunction

A compound statement containing the word or. will always be true unless both simple statements are false.

proper subset

A more restricted type of subset when one element is not contained in the subset

equivalent sets

When two finite sets have the same cardinal number, that is, the same number of elements

quantifiers

all, some, none, or no

union

combination of the elements of two or more sets together

complement of set A

consists of all the elements in the given universal set that are not contained in A. Denoted by A′

finite set

has a specific number of elements

ℤ represents

integers: ... -2, -1, 0, 1, 2 ...

compound statement

is composed of two or more statements joined together using connective words such as and, or, or implies.

cardinal number

is the number of elements contained in a finite set, or in other words, the size of the set

ℕ represents

natural numbers: 1, 2, 3, 4 ...

Biconditional statements

read "if and only if," are true only when each component of the statement has the same truth value; that is, either both are true or both are false.

ℝ represents

real numbers: ... -3, -2.5, -1, 0, 1.5, 2, 3.6 ...

De Morgan's Laws

show how a negation sign is "distributed" across compound statements.

Logically equivalent statements

statements that have exactly the same truth values in all situations. We write this mathematically using the symbol ≡.

Survey analysis

the analysis of responses to a list of questions.

Contrapositive

the flip and negation of a compound statement

converse

the flip of a compound statement

commonality

the intersection of the sets

negation

the logical opposite of that statement, or its denial. always have the opposite truth value of the original statement

inverse

the negation of a compound statement

intersection

the set of all elements common to both A and B.

universal set

the set of all elements that are being considered in any particular situation, denoted by U

disjoint

there are no elements in set A that are also contained in set B. the intersection of two sets is the null, or empty set

equal sets

two sets contain exactly the same elements

Set-builder notation

used to describe a set when the members all share certain properties.

empty set

we denote this symbolically by writing A=∅,or A={ }. The cardinality is 0.

𝕎 represents

whole numbers: 0, 1, 2, 3, 4 ...

Cardinal number; 2n; 2n-1

___________________ of a set is n , then there are _________ subsets and ____________ proper subsets contained in the set.

set

a collection of objects made up of specified elements, or members.

Mathematical statement

a complete sentence that asserts a claim that is either true or false, but not both at the same time

conditional

a compound statement where a and b are statements, then "if a, then b" is always be true unless a is true and b is false.

conjunction

a compound statement where two simple statements are joined with the word and. is true only when both statements are true; otherwise it is false.

Paradoxes

a sentence that contradicts itself and therefore has no single truth value and are not allowed to be statements because they have no truth value

ellipsis

a series of three dots

subset

a set contained within another

tautology

a statement that is true in all possible circumstances.

truth table

a table that has a row for each possible combination of truth values of the individual statements that make up the compound statement.

Roster notation

a way to describe a set by listing all of the elements in the set.

Venn diagram

a way to visualize the relationships between sets