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